Illusion pages | Warning: This page contains some works of "anomalous motion illusion", which might make sensitive observers dizzy or sick.



What Will Life Be Like in the Year 2008? (Nov, 1968)

Well, we do have flat-screen computers you can write on that fit in a briefcase, but I’m still waiting to take my 250 MPH car to a business meeting in another domed city. Perhaps by the end of the year.


40 Years in the Future

By James R. Berry

IT’S 8 a.m., Tuesday, Nov. 18, 2008, and you are headed for a business appointment 300 mi. away. You slide into your sleek, two-passenger air-cushion car, press a sequence of buttons and the national traffic computer notes your destination, figures out the current traffic situation and signals your car to slide out of the garage. Hands free, you sit back and begin to read the morning paper—which is flashed on a flat TV screen over the car’s dashboard. Tapping a button changes the page.

The car accelerates to 150 mph in the city’s suburbs, then hits 250 mph in less built-up areas, gliding over the smooth plastic road. You whizz past a string of cities, many of them covered by the new domes that keep them evenly climatized year round. Traffic is heavy, typically, but there’s no need to worry. The traffic computer, which feeds and receives signals to and from all cars in transit between cities, keeps vehicles at least 50 yds. apart. There hasn’t been an accident since the system was inaugurated. Suddenly your TV phone buzzes. A business associate wants a sketch of a new kind of impeller your firm is putting out for sports boats. You reach for your attache case and draw the diagram with a pencil-thin infrared flashlight on what looks like a TV screen lining the back of the case. The diagram is relayed to a similar screen in your associate’s office, 200 mi. away. He jabs a button and a fixed copy of the sketch rolls out of the device. He wishes you good luck at the coming meeting and signs off.

Ninety minutes after leaving your home, you slide beneath the dome of your destination city. Your car decelerates and heads for an outer-core office building where you’ll meet your colleagues. After you get out, the vehicle parks itself in a convenient municipal garage to await your return. Private cars are banned inside most city cores. Moving sidewalks and electrams carry the public from one location to another.

With the U.S. population having soared to 350 million, 2008 transportation is among the most important factors keeping the economy running smoothly. Giant transportation hubs called modemixers are located anywhere from 15 to 50 mi. outside all major urban centers. Tube trains, pushed through bores by compressed air, make the trip between modemixer and central city in 10 to 15 minutes.

A major feature of most modemixers is the launching pad from which 200-passenger rockets blast off for other continents. For less well-heeled travelers there are SST and hypersonic planes that carry 200 to 300 passengers at speeds up to 4,000 mph. Short trips— between cities less than 1,000 mi. apart—are handled by slower jumbo jets.

Homes in Mi’s 80th year are practically self-maintaining. Electrostatic precipitators clean the air and climatizers maintain the temperature and humidity at optimum levels. Robots are available to do housework and other simple chores. New materials for siding and interiors are self-cleaning and never peel, chip or crack.

Dwellings for the most part are assembled from prefabricated modules, which can be attached speedily in the configuration that best suits the homeowner. Once the foundation is laid, attaching the modules to make up a two- or three-bedroom house is a job that doesn’t take more than a day. Such modular homes easily can be expanded to accommodate a growing family. A typical wedding present for the 21st century newlyweds is a fully equipped bedroom, kitchen or living room module.

Other conveniences ease kitchenwork. The housewife simply determines in advance her menus for the week, then slips prepackaged meals into the freezer and lets the automatic food utility do the rest. At preset times, each meal slides into the microwave oven and is cooked or thawed. The meal then is served on disposable plastic plates. These plates, as well as knives, forks and spoons of the same material, are so inexpensive they can be discarded after use.

The single most important item in 2008 households is the computer. These electronic brains govern everything from meal preparation and waking up the household to assembling shopping lists and keeping track of the bank balance. Sensors in kitchen appliances, climatizing units, communicators, power supply and other household utilities warn the computer when the item is likely to fail. A repairman will show up even before any obvious breakdown occurs.

Computers also handle travel reservations, relay telephone messages, keep track of birthdays and anniversaries, compute taxes and even figure the monthly bills for electricity, water, telephone and other utilities. Not every family has its private computer. Many families reserve time on a city or regional computer to serve their needs. The machine tallies up its own services and submits a bill, just as it does with other utilities.

Money has all but disappeared. Employers deposit salary checks directly into their employees’ accounts. Credit cards are used for paying all bills. Each time you buy something, the card’s number is fed into the store’s computer station. A master computer then deducts the charge from your bank balance.

Computers not only keep track of money, they make spending it easier. TV-telephone shopping is common. To shop, you simply press the numbered code of a giant shopping center. You press another combination to zero in on the department and the merchandise in which you are interested. When you see what you want, you press a number that signifies “buy,” and the household computer takes over, places the order, notifies the store of the home address and subtracts the purchase price from your bank balance. Much of the family shopping is done this way. Instead of being jostled by crowds, shoppers electronically browse through the merchandise of any number of stores.

People have more time for leisure activities in the year 2008. The average work day is about four hours. But the extra time isn’t totally free. The pace of technological advance is such that a certain amount of a jobholder’s spare time is used in keeping up with the new developments—on the average, about two hours of home study a day.

Most of this study is in the form of programmed TV courses, which can be rented or borrowed from tape _ * libraries. In fact most schooling—from first grade through college—consists of programmed TV courses or lectures via closed circuit. Students visit a campus once or twice a week for personal consultations or for lab work that has to be done on site. Progress of each student is followed by computer, which assigns end term marks on the basis of tests given throughout the term.

Besides school lessons, other educational material is available for TV viewing. You simply press a combination of buttons and the pages flash on your home screen. The world’s information is available to you almost instantaneously.

TV screens cover an entire wall in most homes and show most subjects other than straight text matter in color and three dimensions. In addition to programmed TV and the multiplicity of commercial fare, you can see top Broadway shows, hit movies and current nightclub acts for a nominal charge. Best-selling books are on TV tape and can be borrowed or rented from tape libraries.

A typical vacation in 2008 is to spend a week at an undersea resort, where your hotel room window looks out on a tropical underwater reef, a sunken ship or an ancient, excavated city. Available to guests are two- and three-person submarines in which you can cruise well-marked underwater trails.

Another vacation is a stay <>

While city life in 2008 has changed greatly, the farm has altered even more. Farmers are business executives running operations as automated as factories. TV scanners monitor tractors and other equipment computer programmed to plow, harrow and harvest. Wires imbedded in the ground send control signals to the machines. Computers also keep track of yields-, fertilization, soil composition and other factors influencing crops. At the beginning of each year, a print-out tells the farmer what to plant where, how much to fertilize and how much yield he can expect.

Farming isn't confined to land. Mariculturists have turned areas of the sea into beds of protein-rich seaweed and algae. This raw material is processed into food that looks and tastes like steak and other meats. It also is cheap; families can have steak-like meals twice a day without feeling a budget pinch. Areas in bays or close to shore have been turned into shrimp, lobster, clam and other shellfish ranches, like the cattle spreads of yesteryear.

Medical research has guaranteed that most babies born in the 21st century will live long and healthy lives. Heart disease has virtually been eliminated by drugs and diet. If hearts or other major organs do give trouble, they can be replaced with artificial organs.

Medical examinations are a matter of sitting in a diagnostic chair for a minute or two, then receiving a full health report. Ultrasensitive microphones and electronic sensors in the chair's headrest, back and armrests pick up heartbeat, pulse, breathing rate, galvanic skin response, blood pressure, nerve reflexes and other medical signs. A computer attached to the chair digests these responses, compares them to the normal standard and prints out a full medical report.

No need to worry about failing memory or intelligence either. The intelligence pill is another 21st century commodity. Slow learners or people struck with forgetful-ness are given pills which increase the production of enzymes controlling production of the chemicals known to control learning and memory. Everyone is able to use his full mental potential.

Despite the fact that the year 2008 is only 40 years away—as far ahead as 1928 is in the past—it will be a world as strange to us as our time (1968) would be to the pilgrims. •

Funny Responses on Student Exams

  1. "When you breath, you inspire. When you do not breath, you expire."
  2. "H2O is hot water, and CO2 is cold water"
  3. "To collect fumes of sulphur, hold a deacon over a flame in a test tube"
  4. "When you smell an oderless gas, it is probably carbon monoxide"
  5. "Nitrogen is not found in Ireland because it is not found in a free state"
  6. "Water is composed of two gins, Oxygin and Hydrogin. Oxygin is pure gin. Hydrogin is gin and water."
  7. "Three kinds of blood vessels are arteries, vanes and caterpillars."
  8. "Blood flows down one leg and up the other."
  9. "Respiration is composed of two acts, first inspiration, and then expectoration."
  10. "The moon is a planet just like the earth, only it is even deader."
  11. "Artifical insemination is when the farmer does it to the cow instead of the bull."
  12. "Dew is formed on leaves when the sun shines down on them and makes them perspire."
  13. "A super-saturated solution is one that holds more than it can hold."
  14. "Mushrooms always grow in damp places and so they look like umbrellas."
  15. "The body consists of three parts- the brainium, the borax and the abominable cavity. The brainium contains the brain, the borax contains the heart and lungs, and the abominable cavity contains the bowls, of which there are five - a, e, i, o, and u."
  16. "The pistol of a flower is its only protection against insects."
  17. "The alimentary canal is located in the northern part of Indiana."
  18. "The skeleton is what is left after the insides have been taken out and the outsides have been taken off. The purpose of the skeleton is something to hitch meat to."
  19. "A permanent set of teeth consists of eight canines, eight cuspids, two molars, and eight cuspidors."
  20. "The tides are a fight between the Earth and moon. All water tends towards the moon, because there is no water in the moon, and nature abhors a vacuum. I forget where the sun joins in this fight."
  21. "A fossil is an extinct animal. The older it is, the more extinct it is."
  22. "Many women belive that an alcoholic binge will have no ill effects on the unborn fetus, but that is a large misconception."
  23. "Equator: A managerie lion running around the Earth through Africa."
  24. "Germinate: To become a naturalized German."
  25. "Liter: A nest of young puppies."
  26. "Magnet: Something you find crawling all over a dead cat."
  27. "Momentum: What you give a person when they are going away."
  28. "Planet: A body of Earth surrounded by sky."
  29. "Rhubarb: A kind of celery gone bloodshot."
  30. "Vacumm: A large, empty space where the pope lives."
  31. "Before giving a blood transfusion, find out if the blood is affirmative or negative."
  32. "To remove dust from the eye, pull the eye down over the nose."
  33. "For a nosebleed: Put the nose much lower then the body until the heart stops."
  34. "For drowning: Climb on top of the person and move up and down to make artifical perspiration."
  35. "For fainting: Rub the person's chest or, if a lady, rub her arm above the hand instead. Or put the head between the knees of the nearest medical doctor."
  36. "For dog bite: put the dog away for sevral days. If he has not recovered, then kill it."
  37. "For asphyxiation: Apply artificial respiration until the patient is dead."
  38. "To prevent contraception: wear a condominium."
  39. "For head cold: use an agonizer to spray the nose untill it drops in your throat."
  40. "To keep milk from turning sour: Keep it in the cow."

Amazing Facts about the Human Body

The human body is a machine that is full of wonder. This collection of human body facts will leave you wondering why in the heck we were designed the way we were.

Scientists say the higher your I.Q. the more you dream.

The largest cell in the human body is the female egg and the smallest is the male sperm.

You use 200 muscles to take one step.

The average woman is 5 inches shorter than the average man.

Your big toes have two bones each while the rest have three.

A pair of human feet contain 250,000 sweat glands.

A full bladder is roughly the size of a soft ball.

The acid in your stomach is strong enough to dissolve razor blades.

The human brain cell can hold 5 times as much information as the Encyclopedia Britannica.

It takes the food seven seconds to get from your mouth to your stomach.

The average human dream lasts 2-3 seconds

Men without hair on their chests are more likely to get cirrhosis of the liver than men with hair.

At the moment of conception, you spent about half an hour as a single cell.

There is about one trillion bacteria on each of your feet.

Your body gives off enough heat in 30 minutes to bring half a gallon of water to a boil.

The enamel in your teeth is the hardest substance in your body.

Your teeth start growing 6 months before you are born.

When you are looking at someone you love, your pupils dilate, they do the same when you are looking at someone you hate.



Blondes have more hair than dark-haired people.

Your thumb is the same length of your nose.

Now I KNOW you are placing your thumb on your NOSE, aren't you?

What's Special About This Number?

0 is the additive identity.
1 is the multiplicative identity.
2 is the only even prime.
3 is the number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
11 is the largest known multiplicative persistence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.
15 is the smallest composite number n with the property that there is only one group of order n.
16 is the only number of the form xy = yx with x and y different integers.
17 is the number of wallpaper groups.
18 is the only number (other than 0) that is twice the sum of its digits.
19 is the maximum number of 4th powers needed to sum to any number.
20 is the number of rooted trees with 6 vertices.
21 is the smallest number of distinct squares needed to tile a square.
22 is the number of partitions of 8.
23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
24 is the largest number divisible by all numbers less than its square root.
25 is the smallest square that can be written as a sum of 2 squares.
26 is the only positive number to be directly between a square and a cube.
27 is the largest number that is the sum of the digits of its cube.
28 is the 2nd perfect number.
29 is the 7th Lucas number.
30 is the largest number with the property that all smaller numbers relatively prime to it are prime.
31 is a Mersenne prime.
32 is the smallest non-trivial 5th power.
33 is the largest number that is not a sum of distinct triangular numbers.
34 is the smallest number with the property that it and its neighbors have the same number of divisors.
35 is the number of hexominoes.
36 is the smallest non-trivial number which is both square and triangular.
37 is the maximum number of 5th powers needed to sum to any number.
38 is the last Roman numeral when written lexicographically.
39 is the smallest number which has 3 different partitions into 3 parts with the same product.
40 is the only number whose letters are in alphabetical order.
41 is a value of n so that x2 + x + n takes on prime values for x=0, 1, 2, ... n-2.
42 is the 5th Catalan number.
43 is the number of sided 7-iamonds.
44 is the number of derangements of 5 items.
45 is a Kaprekar number.
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.
47 is the largest number of cubes that cannot tile a cube.
48 is the smallest number with 10 divisors.
49 is the smallest number with the property that it and its neighbors are squareful.
50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.
51 is the 6th Motzkin number.
52 is the 5th Bell number.
53 is the only two digit number that is reversed in hexadecimal.
54 is the smallest number that can be written as the sum of 3 squares in 3 ways.
55 is the largest triangular number in the Fibonacci sequence.
56 is the number of reduced 5×5 Latin squares.
57 = 111 in base 7.
58 is the number of commutative semigroups of order 4.
59 is the number of stellations of an icosahedron.
60 is the smallest number divisible by 1 through 6.
61 is the 6th Euler number.
62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.
63 is the number of partially ordered sets of 5 elements.
64 is the smallest number with 7 divisors.
65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.
66 is the number of 8-iamonds.
67 is the smallest number which is palindromic in bases 5 and 6.
68 is the 2-digit string that appears latest in the decimal expansion of π.
69 has the property that n2 and n3 together contain each digit once.
70 is the smallest weird number.
71 divides the sum of the primes less than it.
72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.
73 is the smallest multi-digit number which is one less than twice its reverse.
74 is the number of different non-Hamiltonian polyhedra with minimum number of vertices.
75 is the number of orderings of 4 objects with ties allowed.
76 is an automorphic number.
77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.
79 is a permutable prime.
80 is the smallest number n where n and n+1 are both products of 4 or more primes.
81 is the square of the sum of its digits.
82 is the number of 6-hexes.
83 is the number of zero-less pandigital squares.
84 is the largest order of a permutation of 14 elements.
85 is the largest n for which 12+22+32+ ... +n2 = 1+2+3+ ... +m has a solution.
86 = 222 in base 6.
87 is the sum of the squares of the first 4 primes.
88 is the only number known whose square has no isolated digits.
89 = 81 + 92
90 is the number of degrees in a right angle.
91 is the smallest pseudoprime in base 3.
92 is the number of different arrangements of 8 non-attacking queens on an 8×8 chessboard.
93 = 333 in base 5.
94 is a Smith number.
95 is the number of planar partitions of 10.
96 is the smallest number that can be written as the difference of 2 squares in 4 ways.
97 is the smallest number with the property that its first 3 multiples contain the digit 9.
98 is the smallest number with the property that its first 5 multiples contain the digit 9.
99 is a Kaprekar number.
100 is the smallest square which is also the sum of 4 consecutive cubes.
101 is the number of partitions of 13.
102 is the smallest number with three different digits.
103 has the property that placing the last digit first gives 1 more than triple it.
104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.
105 is the largest number n known with the property that n - 2k is prime for k>1.
106 is the number of trees with 10 vertices.
107 is the exponent of a Mersenne prime.
108 is 3 hyperfactorial.
109 has a 5th root that starts 2.555555....
110 is the smallest number that is the product of two different substrings.
111 is the smallest possible magic constant of a 3×3 magic square of distinct primes.
112 is the side of the smallest square that can be tiled with distinct integer-sided squares.
113 is a permutable prime.
114 = 222 in base 7.
115 is the number of rooted trees with 8 vertices.
116 is a value of n for which n! + 1 is prime.
117 is the smallest possible value of the longest edge in a Heronian Tetrahedron.
118 is the smallest number that has 4 different partitions into 3 parts with the same product.
119 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 8.
120 is the smallest number to appear 6 times in Pascal's triangle.
121 is the only square known of the form 1 + p + p2 + p3 + p4, where p is prime.
122 is the smallest number n>1 so that n concatenated with n-1 0's concatenated with the reverse of n is prime.
123 is the 10th Lucas number.
124 is the smallest number with the property that its first 3 multiples contain the digit 2.
125 is the only number known that contains all its proper divisors as proper substrings.
126 = 9C4.
127 is a Mersenne prime.
128 is the largest number which is not the sum of distinct squares.
129 is the smallest number that can be written as the sum of 3 squares in 4 ways.
130 is the number of functions from 6 unlabeled points to themselves.
131 is a permutable prime.
132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.
133 is the smallest number n for which the sum of the proper divisors of n divides φ(n).
134 = 8C1 + 8C3 + 8C4.
135 = 11 + 32 + 53.
136 is the sum of the cubes of the digits of the sum of the cubes of its digits.
137 is the smallest prime with 3 distinct digits that remains prime if one of its digits is removed.
138 is a value of n for which n!!! - 1 is prime.
139 is the number of unlabeled topologies with 5 elements.
140 is the smallest harmonic divisor number.
141 is the 6th central trinomial coefficient.
142 is the number of planar graphs with 6 vertices.
143 is the smallest quasi-Carmichael number in base 8.
144 is the largest square in the Fibonacci sequence.
145 is a factorion.
146 = 222 in base 8.
147 is the number of sided 6-hexes.
148 is the number of perfect graphs with 6 vertices.
149 is the smallest number whose square begins with three 2's.
150 = 100101102 = 21124 = 11005, each using 2 different digits an equal number of times.
151 is a palindromic prime.
152 has a square composed of the digits 0-4.
153 is a narcissistic number.
154 is the smallest number which is palindromic in bases 6, 8, and 9.
155 is the sum of the primes between its smallest and largest prime factor.
156 is the number of graphs with 6 vertices.
157 is the largest number known whose square contains the same digits as the square of its successor.
158 is the number of planar partitions of 11.
159 is the number of isomers of C11H24.
160 is the number of 9-iamonds.
161 is a Cullen number.
162 is the smallest number that can be written as the sum of of 4 positive squares in 9 ways.
163 is the largest Heegner Number.
164 is the smallest number which is the concatenation of squares in two different ways.
165 = 11C3.
166 is the number of monotone Boolean functions of 4 variables.
167 is the smallest number whose 4th power begins with 4 identical digits
168 is the size of the smallest non-cyclic simple group which is not an alternating group.
169 is the 7th Pell number.
170 is the smallest number n for which φ(n) and σ(n) are both square.
171 has the same number of digits in Roman numerals as its cube.
172 = 444 in base 6.
173 has a square containing only 2 digits.
174 is the smallest number that can be written as the sum of of 4 positive distinct squares in 6 ways.
175 = 11 + 72 + 53.
176 is an octagonal pentagonal number.
177 is the number of graphs with 7 edges.
178 has a cube with the same digits as another cube.
179 has a square comprised of the digits 0-4.
180 is the total number of degrees in a triangle.
181 is a strobogrammatic prime.
182 is the number of connected bipartite graphs with 8 vertices.
183 is the smallest number n so that n concatenated with n+1 is square.
184 is a Kaprekar constant in base 3.
185 is the number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.
186 is the number of degree 11 irreducible polynomials over GF(2).
187 is the smallest quasi-Carmichael number in base 7.
188 is the number of semigroups of order 4.
189 is a Kaprekar constant in base 2.
190 is the largest number with the property that it and its ditinct prime factors are palindromic in Roman numerals.
191 is a number n for which n, n+2, n+6, and n+8 are all prime.
192 is the smallest number with 14 divisors.
193 is the largest number that can be written as ab + ac + bc with 0 < a < b < c in a unique way.
194 is the smallest number that can be written as the sum of 3 squares in 5 ways.
195 is the smallest value of n such that 2nCn is divisible by n2.
196 is the smallest number that is not known to reach a palindrome when repeatedly added to its reverse.
197 is a Keith number.
198 = 11 + 99 + 88.
199 is the 11th Lucas number.
200 is the smallest number which can not be made prime by changing one of its digits.
201 is a Kaprekar constant in base 4.
202 has a cube that contains only even digits.
203 is the 6th Bell number.
204 is the square root of a triangular number.
205 is the largest number which can not be writen as the sum of distinct primes of the form 6n+1.
206 is the smallest number whose English name contains all five vowels exactly once.
207 has a 4th power where the first half of the digits are a permutation of the last half of the digits.
208 is the 10th tetranacci number.
209 is the smallest quasi-Carmichael number in base 9.
210 is the product of the first 4 primes.
211 has a cube containing only 3 different digits.
212 has a square with 4/5 of the digits are the same.
213 is the number of perfect squared rectangles of order 13.
214 is a value of n for which n!! - 1 is prime.
215 = 555 in base 6.
216 is the smallest cube that can be written as the sum of 3 cubes.
217 is a Kaprekar constant in base 2.
218 is the number of digraphs with 4 vertices.
219 is the number of space groups, not including handedness.
220 is the smallest amicable number.
221 is the number of Hamiltonian planar graphs with 7 vertices.
222 is the number of lattices on 8 unlabeled nodes.
223 is the smallest prime which will nor remain prime if one of its digits is changed.
224 is not the sum of 4 non-zero squares.
225 is an octagonal square number.
226 are the first 3 digits of π226.
227 is the number of connected planar graphs with 8 edges.
228 is the number of ways, up to rotation and reflection, of dissecting a regular 11-gon into 9 triangles.
229 is the smallest prime that remains prime when added to its reverse.
230 is the number of space groups, including handedness.
231 is the number of partitions of 16.
232 is the number of 7×7 symmetric permutation matrices.
233 is the smallest number with the property that it and its neighbors can be written as a sum of 2 squares.
234 has consecutive digits.
235 is the number of trees with 11 vertices.
236 is the number of Hamiltonian circuits of a 4×8 rectangle.
237 is the smallest number with the property that its first 3 multiples contain the digit 7.
238 is the number of connected partial orders on 6 unlabeled elements.
239 is the largest number that cannot be written as a sum of 8 or fewer cubes.
240 is the smallest number with 20 divisors.
241 is the only number n for which the nth prime is π(n π(n)).
242 is the smallest n for which n, n+1, n+2, and n+3 have the same number of divisors.
243 = 35.
244 is the smallest number (besides 2) that can be written as the sum of 2 squares or the sum of two 5th powers.
245 is a stella octangula number.
246 = 9C2 + 9C4 + 9C6.
247 is the smallest possible difference between two integers that together contain each digit exactly once.
248 is the smallest number n>1 for which the arithmetic, geometric, and harmonic means of φ(n) and σ(n) are all integers.
249 is the index of a prime Woodall number.
250 is the smallest multi-digit number so that the sum of the squares of its prime factors equals the sum of the squares of its digits.
251 is the smallest number that can be written as the sum of 3 cubes in 2 ways.
252 is the 5th central binomial coefficient.
253 is the smallest non-trivial triangular star number.
254 is the smallest composite number all of whose proper divisors contain the digit 2.
255 = 11111111 in base 2.
256 is the smallest non-trivial 8th power.
257 is a Fermat prime.
258 is a value of n so that n(n+9) is a palindrome.
259 = 1111 in base 6.
260 is the number of ways that 6 non-attacking bishops can be placed on a 4×4 chessboard.
261 is the number of essentially different ways to dissect a 16-gon into 7 quadrilaterals.
262 is the 5th meandric number and the 9th open meandric number.
263 is the largest known prime whose square is strobogrammatic.
264 is the largest known number whose square is undulating.
265 is the number of derangements of 6 items.
266 is the Stirling number of the second kind S(8,6).
267 is the number of planar partitions of 12.
268 is the smallest number whose product of digits is 6 times the sum of its digits.
269 is the number of 6-octs.
270 is a harmonic divisor number.
271 is the smallest prime p so that p-1 and p+1 are divisible by cubes.
272 is the 7th Euler number.
273 = 333 in base 9.
274 is the Stirling number of the first kind s(6,2).
275 is the number of partitions of 28 in which no part occurs only once.
276 is the sum of the first three 5th powers.
277 is a Perrin number.
278 is the closest integer to 6π.
279 is the maximum number of 8th powers needed to sum to any number.
280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.
281 is the sum of the first 14 primes.
282 is the number of planar partitions of 9.
283 = 25 + 8 + 35.
284 is an amicable number.
285 is the number of binary rooted trees with 13 vertices.
286 is the number of rooted trees with 9 vertices.
287 is the sum of consecutive primes in 3 different ways.
288 is the smallest non-palindrome non-square that when multiplied by its reverse is a square.
289 is a Friedman number.
290 has a base 3 representation that ends with its base 6 representation.
291 is the largest number that is not the sum of distinct non-trivial powers.
292 is the number of ways to make change for a dollar.
293 is the number of ways to have one dollar in coins.
294 is the number of planar 2-connected graphs with 7 vertices.
295 is a structured deltoidal hexacontahedral number.
296 is the number of partitions of 30 into distinct parts.
297 is a Kaprekar number.
298 is a value of n so that n(n+3) is a palindrome.
299 is the maximum number of regions a cube can be cut into with 12 cuts.
300 is the largest possible score in bowling.
301 is a 6-hyperperfect number.
302 is the number of acyclic digraphs with 5 vertices.
303 has a cube that is a concatenation of other cubes.
304 is a primitive semiperfect number.
305 is an hexagonal prism number.
306 is the number of 5-digit triangular numbers.
307 is a non-palindrome with a palindromic square.
308 is a heptagonal pyramidal number.
309 is the smallest number whose 5th power contains every digit at least once.
310 = 1234 in base 6.
311 is a permutable prime.
312 = 2222 in base 5.
313 is the number of intersections when all the diagonals of a regular dodecagon are drawn.
314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways.
315 = (4+3) × (4+1) × (4+5).
316 has a digit product which is the digit sum of 31×6.
317 is a value of n for which one less than the product of the first n primes is prime.
318 is the number of unlabeled partially ordered sets of 6 elements.
319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts.
320 is the maximum determinant of a 10×10 matrix of 0's and 1's.
321 is a Delannoy number.
322 is the 12th Lucas number.
323 is the product of twin primes.
324 is the largest possible product of positive integers with sum 16.
325 is a 3-hyperperfect number.
326 is the number of permutations of some subset of 5 elements.
327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once.
328 concatenated with its successor is square.
329 is the number of forests with 10 vertices.
330 = 11C4.
331 is both a centered pentagonal number and a centered hexagonal number.
332 ???
333 is the number of 7-hexes.
334 is the number of trees on 13 vertices with diameter 7.
335 is the number of degree 12 irreducible polynomials over GF(2).
336 = 8P3.
337 is a permutable prime.
338 ???
339 is the number of ways to divide 5 black and 5 white beads into piles.
340 is a value of n for which n! + 1 is prime.
341 is the smallest pseudoprime in base 2.
342 = 666 in base 7.
343 is a strong Friedman number.
344 is the number of different arrangements of 4 non-attacking queens on a 4×8 chessboard.
345 is half again as large as the sum of its proper divisors.
346 is a Franel number.
347 is a Friedman number.
348 is the smallest number whose 5th power contains exactly the same digits as another 5th power.
349 is a tetranacci number.
350 is the Stirling number of the second kind S(7,4).
351 is the smallest number so that it and the surrounding numbers are all products of 4 or more primes.
352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard.
353 is the smallest number whose 4th power can be written as the sum of four 4th powers.
354 is the sum of the first four 4th powers.
355 is the number of labeled topologies with 4 elements.
356 ???
357 has a base 3 representation that ends with its base 7 representation.
358 has a base 3 representation that ends with its base 7 representation.
359 has a base 3 representation that ends with its base 7 representation.
360 is the number of degrees in a circle.
361 is the number of intersections on a go board.
362 and its double and triple all use the same number of digits in Roman numerals.
363 is a perfect totient number.
364 = 14C3.
365 is the smallest number that can be written as a sum of consecutive squares in more than 1 way.
366 is the number of days in a leap year.
367 is the largest number whose square has strictly increasing digits.
368 is the number of ways to tile a 4×15 rectangle with the pentominoes.
369 is the number of octominoes.
370 is a narcissistic number.
371 is a narcissistic number.
372 is a hexagonal pyramidal number.
373 is a permutable prime.
374 is the smallest number that can be written as the sum of 3 squares in 8 ways.
375 is a truncated tetrahedral number.
376 is an automorphic number.
377 is the 14th Fibonacci number.
378 is the maximum number of regions a cube can be cut into with 13 cuts.
379 is a value of n for which one more than the product of the first n primes is prime.
380 is the number of necklaces possible with 13 beads, each being one of 2 colors.
381 is a Kaprekar constant in base 2.
382 is the smallest number n with σ(n) = σ(n+3).
383 is the number of Hamiltonian graphs with 7 vertices.
384 = 8!! = 12!!!!.
385 is the number of partitions of 18.
386 is the number of regions the complex plane is cut into by drawing lines between all pairs of 11th roots of unity.
387 ???
388 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps.
389 is the smallest prime so that it and the next 3 primes are all equal to 1 (mod 4).
390 is the number of partitions of 32 into distinct parts.
391 ???
392 is a Kaprekar constant in base 5.
393 is the 7th central trinomial coefficient.
394 is a Schröder number.
395 ???
396 is the number of 3×3 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.
397 is a Cuban prime.
398 ???
399 is a value of n for which n! + 1 is prime.
400 = 1111 in base 7.
401 is the number of connected planar Eulerian graphs with 9 vertices.
402 ???
403 is the product of two primes which are reverses of each other.
404 is the number of sided 10-hexes with holes.
405 is a pentagonal pyramidal number.
406 is the number of ways to tile a 3×17 rectangle with 3×1 rectangles.
407 is a narcissistic number.
408 is the 8th Pell number.
409 ???
410 is the smallest number that can written as the sum of 2 distinct prime powers in 2 ways.
411 is the number of triangles of any size contained in the triangle of side 11 on a triangular grid.
412 ???
413 ???
414 is a palindrome in base 8 and in base 10.
415 ???
416 is the number of subsets of the 15th roots of unity that add to a real number.
417 ???
418 has the property that the sum of its prime factors is equal to the product of its digits.
419 ???
420 is the smallest number divisible by 1 through 7.
421 is the number of commutative monoids of order 6.
422 ???
423 is a number that does not have any digits in common with its cube.
424 ???
425 is the number of subsets of {1,2,3,...,11} that have an integer average.
426 is a stella octangula number.
427 is a value of n for which n! + 1 is prime.
428 has the property that its square is the concatenation of two consecutive numbers.
429 is the 7th Catalan number.
430 is the number of necklaces possible with 6 beads, each being one of 4 colors.
431 is the index of a prime Fibonacci number.
432 = 4 × 33 × 22.
433 is the index of a prime Fibonacci number.
434 is the smallest composite value of n for which σ(n) + 2 = σ(n+2).
435 ???
436 ???
437 has a cube with the last 3 digits the same as the 3 digits before that.
438 = 666 in base 8.
439 is the smallest prime where inserting the same digit between every pair of digits never yields another prime.
440 is the number of permutations of 12 items that fix 9 elements.
441 is the smallest square which is the sum of 6 consecutive cubes.
442 is the number of planar partitions of 13.
443 ???
444 is the largest known n for which there is a unique integer solution to a1+ ... +an = (a1)...(an).
445 has a base 10 representation which is the reverse of its base 9 representation.
446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.
447 is the smallest number of convex quadrilaterals formed by 15 points in general position.
448 is the number of 10-iamonds.
449 has a base 3 representation that begins with its base 7 representation.
450 is the number of 13-iamonds with holes.
451 is the smallest number whose reciprocal has period 10.
452 is the closest integer to 7π.
453 is the only number n so that n, 2n, and 6n together contain every digit exactly once.
454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.
455 = 15C3.
456 is the number of tournaments with 7 vertices.
457 ???
458 is a number that does not have any digits in common with its cube.
459 ???
460 ???
461 = 444 + 6 + 11.
462 = 11C5.
463 is the smallest prime so that it and the next 6 primes are all equal to 3 (mod 4).
464 is the maximum number of regions space can be divided into by 12 spheres.
465 is a Kaprekar constant in base 2.
466 = 1234 in base 7.
467 has strictly increasing digits in bases 7, 9, and 10.
468 = 3333 in base 5.
469 is the largest known value of n for which n!-1 is prime.
470 has a base 3 representation that ends with its base 6 representation.
471 is the smallest number with the property that its first 4 multiples contain the digit 4.
472 is the number of ways to tile a 5×5 square with integer-sided squares.
473 is the largest known number whose square and 4th power use different digits.
474 ???
475 has a square that is composed of overlapping squares of smaller numbers.
476 is the number of different products of subsets of the set {1, 2, 3, ... 11}.
477 ???
478 is the 7th Pell-Lucas number.
479 is the number of sets of distinct positive integers with mean 6.
480 is the smallest number which can be written as the difference of 2 squares in 8 ways.
481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube.
482 is a number whose square and cube use different digits.
483 is the last 3-digit string in the decimal expansion of π.
484 is a palindrome in base 3 and in base 10.
485 ???
486 is a Perrin number.
487 is the number of Hadamard matrices of order 28.
489 is an octahedral number.
490 is the number of partitions of 19.
491 ???
492 is a hexanacci number.
493 ???
494 ???
495 is the Kaprekar constant for 3-digit numbers.
496 is the 3rd perfect number.
497 is the number of graphs with 8 edges.
498 is the number of necklaces possible with 8 beads, each being one of 3 colors.
499 is the smallest number with the property that its first 12 multiples contain the digit 9.
500 is the number of planar partitions of 10.
501 is the number of partitions of 5 items into ordered lists.
502 uses the same digits as φ(502).
503 is the smallest prime which is the sum of the cubes of the first few primes.
504 = 9P3.
505 = 10C5 + 10C0 + 10C5.
506 is the sum of the first 11 squares.
507 is the number of rooted ternary trees with 10 vertices.
509 is the index of a prime Fibonacci number.
510 is the number of binary rooted trees with 14 vertices.
511 = 111111111 in base 2.
512 is the cube of the sum of its digits.
513 is the number of conjugacy classes of the alternating group A22.
515 is the number of graphs on 6 vertices with no isolated vertices.
516 is the number of partitions of 32 in which no part occurs only once.
518 = 51 + 12 + 83.
519 is the number of trees on 15 vertices with diameter 5.
520 is the number of ways to place 2 non-attacking kings on a 6×6 chessboard.
521 is the 13th Lucas number.
522 is the number of ways to place a non-attacking white and black pawn on a 6×6 chessboard.
524 is the number of 6-kings.
525 is a hexagonal pyramidal number.
527 is the smallest number n for which there do not exist 4 smaller numbers so that a1! a2! a3! a4! n! is square.
528 concatenated with its successor is square.
529 is the smallest number n so that the continued fraction for n/k contains no 2's for any 1 ≤ k ≤ n.
530 is the sum of the first 3 perfect numbers.
531 is the smallest number with the property that its first 4 multiples contain the digit 1.
532 is a hendecagonal pyramidal number.
535 is a palindrome whose φ(n) is also palindromic.
536 is the number of solutions of the stomachion puzzle.
538 is the 10th open meandric number.
539 is the number of multigraphs with 5 vertices and 9 edges.
540 is divisible by its reverse.
541 is the number of orderings of 5 objects with ties allowed.
543 is a number whose square and cube use different digits.
545 has a base 3 representation that begins with its base 4 representation.
546 undulates in bases 3, 4, and 5.
547 is a Cuban prime.
548 is the maximum number of 9th powers needed to sum to any number.
550 is a pentagonal pyramidal number.
551 is the number of trees with 12 vertices.
552 is the number of prime knots with 11 crossings.
553 is a Huay rhombic dodecahedral number.
554 is the number of self-dual planar graphs with 20 edges.
555 is a repdigit.
556 are the first 3 digits of 4556.
558 divides the sum of the largest prime factors of the first 558 positive integers.
559 is a centered cube number.
560 = 16C3.
561 is the smallest Carmichael number.
562 is the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines.
563 is the largest known Wilson prime.
567 has the property that it and its square together use the digits 1-9 once.
568 is the smallest number whose 7th power can be written as the sum of seven 7th powers.
569 is the smallest number n for which the concatenation of n, (n+1), ... (n+30) is prime.
570 is the product of all the prime palindromic Roman numerals.
571 is the index of a prime Fibonacci number.
572 is the smallest number which has equal numbers of every digit in bases 2 and 3.
573 has the property that its square is the concatenation of two consecutive numbers.
574 is the maximum number of pieces a torus can be cut into with 14 cuts.
575 is a palindrome that is one less than a square.
576 is the number of 4×4 Latin squares.
577 is a Proth prime.
581 has a base 3 representation that begins with its base 4 representation.
582 is the number of antisymmetric relations on a 5 element set.
583 is the smallest number whose reciprocal has period 26.
585 is a palindrome in base 2, base 8, and in base 10.
586 is the smallest number that appears in its factorial 6 times.
587 is the smallest number whose sum of digits is larger than that of its cube.
588 is the number of possible rook moves on a 7×7 chessboard.
589 is a centered tetrahedral number.
590 is a value of n for which φ(n) + φ(n+1) divides σ(n) + σ(n+1).
592 evenly divides the sum of its rotations.
593 is a Leyland number.
594 = 15 + 29 + 34.
595 is the number of ways to tile a 3×18 rectangle with 3×1 rectangles.
596 is the number of Hamiltonian cycles of a 4×9 rectangle graph.
598 = 51 + 92 + 83.
600 and its reverse are both the averages of twin primes.
602 are the first 3 digits of 5602.
604 and the two numbers before it and after it are all products of exactly 3 primes.
605 has a sum of digits equal to its largest prime factor.
607 is the exponent of a Mersenne prime.
608 is a number that does not have any digits in common with its cube.
609 is a strobogrammatic number.
610 is the smallest Fibonacci number that begins with 6.
612 is a number whose square and cube use different digits.
613 is the index of a prime Lucas number.
614 is the smallest number that can be written as the sum of 3 squares in 9 ways.
615 = 555 + 55 + 5.
616 is a Padovan number.
617 = 1!2 + 2!2 + 3!2 + 4!2.
618 is the number of ternary square-free words of length 15.
619 is a strobogrammatic prime.
620 is the number of sided 7-hexes.
621 is the number of ways to 9-color the faces of a tetrahedron.
623 is the number of inequivalent asymmetric Ferrers graphs with 23 points.
624 is the smallest number with the property that its first 5 multiples contain the digit 2.
625 is an automorphic number.
626 is a palindrome in base 5 and in base 10.
627 is the number of partitions of 20.
628 is the sum of the squares of 4 consecutive primes.
629 evenly divides the sum of its rotations.
630 is the number of permutations of 8 items that fix 4 elements.
631 has a base 2 representation that begins with its base 5 representation.
632 is the number of necklaces (that can't be turned over) possible with 13 beads, each being one of 2 colors.
637 = 777 in base 9.
638 is the number of fixed 5-kings.
640 = 16!!!!!!.
641 is the smallest prime factor of 225+1.
642 is the smallest number with the property that its first 6 multiples contain the digit 2.
643 is the largest prime factor of 123456.
644 is a Perrin number.
645 is the largest n for which 1+2+3+ ... +n = 12+22+32+ ... +k2 for some k.
646 is the number of connected planar graphs with 7 vertices.
648 is the smallest number whose decimal part of its 6th root begins with a permutation of the digits 1-9.
650 is the sum of the first 12 squares.
651 has a 4th power that is the sum of four 4th powers.
652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.
653 is the only known prime for which 5 is neither a primitive root or a quadratic residue of 4n2+1.
654 has a square that is the sum of a cube and 5th power.
656 is a palindrome in base 3 and in base 10.
658 is the number of triangles of any size contained in the triangle of side 13 on a triangular grid.
660 is the order of a non-cyclic simple group.
661 is the largest prime factor of 8! + 1.
664 is a value of n so that n(n+7) is a palindrome.
666 is the largest rep-digit triangular number.
667 is the product of two consecutive primes.
668 is the number of legal pawn moves in chess.
670 is an octahedral number.
671 is a rhombic dodecahedral number.
672 is a multi-perfect number.
673 is a tetranacci number.
675 is the smallest order for which there are 17 groups.
676 is the smallest palindromic square number whose square root is not palindromic.
679 is the smallest number with multiplicative persistence 5.
680 is the smallest tetrahedral number that is also the sum of 2 tetrahedral numbers.
682 = 11C6 + 11C8 + 11C2.
683 is a Wagstaff prime.
684 is the sum of 3 consecutive cubes.
686 is the number of partitions of 35 in which no part occurs only once.
687 is the closest integer to 8π.
688 is a Friedman number.
689 is the smallest number that can be written as the sum of 3 distinct squares in 9 ways.
692 is a number that does not have any digits in common with its cube.
694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking rooks on a 7×7 chessboard.
695 is the maximum number of pieces a torus can be cut into with 15 cuts.
696 is a palindrome n so that n(n+8) is also palindromic.
697 is a 12-hyperperfect number.
700 is the number of symmetric 8-cubes.
701 = 10 + 21 + 32 + 43 + 54.
703 is a Kaprekar number.
704 is the number of sided octominoes.
707 is the smallest number whose reciprocal has period 12.
708 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps.
709 is the number of connected planar graphs with 9 edges.
710 is the number of connected graphs with 9 edges.
712 is the largest number known that does not have any digits in common with its 8th power.
714 is the smallest number which has equal numbers of every digit in bases 2 and 5.
715 = 13C4.
717 is a palindrome in base 2 and in base 10.
718 is the number of unlabeled topologies with 6 elements.
719 is the number of rooted trees with 10 vertices.
720 = 6!
721 is the smallest number which can be written as the difference of two cubes in 2 ways.
724 is the number of different arrangements of 10 non-attacking queens on an 10×10 chessboard.
726 is a pentagonal pyramidal number.
727 has the property that its square is the concatenation of two consecutive numbers.
728 is the smallest number n where n and n+1 are both products of 5 or more primes.
729 = 36.
730 is the number of connected bipartite graphs with 9 vertices.
731 is the number of planar partitions of 14.
732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.
733 is the sum of the digits of 444.
734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways.
735 is the smallest number that is the concatenation of its distinct prime factors.
736 is a strong Friedman number.
738 6 + 66 + 666.
739 has a base 2 representation that begins with its base 9 representation.
740 is the number of self-avoiding walks of length 8.
741 is the number of multigraphs with 6 vertices and 8 edges.
742 is the smallest number that is one more than triple its reverse.
743 is the number of independent sets of the graph of the 4-dimensional hypercube.
744 is the number of perfect squared rectangles of order 14.
745 is the smallest number whose square begins with three 5's.
746 = 17 + 24 + 36.
748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.
750 is the Stirling number of the second kind S(10,8).
751 is the index of a prime Woodall number.
752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube.
755 is the number of trees on 14 vertices with diameter 6.
756 is the maximum number of regions space can be divided into by 14 spheres.
757 is the smallest number whose reciprocal has a period of 27.
760 is the number of partitions of 37 into distinct parts.
762 is the first decimal digit of π where a digit occurs four times in a row.
763 is the smallest number whose 4th power contains every digit at least once.
764 is the number of 8×8 symmetric permutation matrices.
765 is a Kaprekar constant in base 2.
767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution.
768 is the number of subsets of {1,2,3,...,12} that have an integer average.
769 is the total number of digits of all binary numbers of length 1-7.
771 is the number of intersections when all the diagonals of a regular 14-gon are drawn.
773 is the smallest odd number n so that n+2k is composite for all k777 is a repdigit in base 6 and in base 10.
778 is the number of ways a 5×1 rectangle can be surrounded by 5×1 rectangles.
780 = (5+7) × (5+8) × (5+0).
781 = 11111 in base 5.
782 is a number whose sum of divisors is a 4th power.
783 is the number of 11-ominoes that tile the plane by translation.
784 is the sum of the first 7 cubes.
786 is the largest known n for which 2nCn is not divisible by the square of an odd prime.
787 is a palindrome in base 3 and in base 10.
788 is the smallest of 6 consecutive numbers divisible by 6 consecutive primes.
789 are the first 4 digits of 9789.
791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12.
792 is the number of partitions of 21.
793 is one less than twice its reverse.
794 is the sum of the first three 6th powers.
795 is a number whose sum of divisors is a 4th power.
797 is the number of functional graphs on 9 vertices.
798 is the number of ternary square-free words of length 16.
800 = 2222 in base 7.
802 is the number of isomers of C13H28.
804 is a value of n for which 2φ(n) = φ(n+1).
808 is a strobogrammatic number.
810 is the number of necklaces with 8 white and 8 black beads.
812 is the number of triangles of any size contained in the triangle of side 14 on a triangular grid.
814 is a value of n so that n(n+5) is a palindrome.
816 = 18C3.
818 is a strobogrammatic number.
819 is the smallest number so that it and its successor are both the product of 2 primes and the square of a prime.
820 = 1111 in base 9.
821 is a number n for which n, n+2, n+6, and n+8 are all prime.
822 is the number of planar graphs with 7 vertices.
823 is a number that does not have any digits in common with its cube.
827 is the number of asymmetric trees with 11 vertices.
832 is the maximum number of pieces a torus can be cut into with 16 cuts.
834 is the maximum number of regions a cube can be cut into with 17 cuts.
835 is the 9th Motzkin number.
836 is a non-palindrome with a palindromic square.
839 has a base 5 representation that begins with its base 9 representation.
840 is the smallest number divisble by 1 through 8.
841 is a square that is also the sum of 2 consecutive squares.
842 is a value of n for which n!! - 1 is prime.
843 is the 14th Lucas number.
844 is the smallest number so that it and the next four numbers are squareful numbers.
846 has the property that its square is the concatenation of two consecutive numbers.
849 is a value of n for which σ(n-1) = σ(n+1).
850 is the number of trees on 14 vertices with diameter 7.
853 is the number of connected graphs with 7 vertices.
854 has the property that it and its square together use the digits 1-9 once.
855 is the smallest number which is the sum of 5 consecutive squares or 2 consecutive cubes.
857 is a value of n for which φ(n) = φ(n-1) + φ(n-2).
858 is the smallest palindrome with 4 different prime factors.
859 is the number of planar partitions of 11.
861 7 + 77 + 777.
862 is a number whose sum of divisors is a 4th power.
863 is a value of n so that n(n+6) is a palindrome.
864 is the number of partitions of 38 into distinct parts.
866 is the number of sided 10-iamonds.
868 has a square root whose decimal part starts with the digits 1-9 in some order.
870 is the sum of its digits and the cube of its digits.
872 is a value of n for which n! + 1 is prime.
873 = 1! + 2! + 3! + 4! + 5! + 6!
875 is 3-automorphic.
877 is the 7th Bell number.
878 is the number of 3×3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on a side.
880 is the number of 4×4 magic squares.
882 is the smallest number whose square begins with three 7's.
888 and the following 18 numbers are composite.
889 is a Kaprekar constant in base 2.
891 is an octahedral number.
894 has a base 5 representation that begins with its base 9 representation.
895 is a Woodall number.
896 is not the sum of 4 non-zero squares.
897 is a Cullen number.
899 is the product of twin primes.
900 has a base 5 representation that begins with its base 9 representation.
901 is the sum of the digits of the first 100 positive integers.
902 is a value of n so that n(n+7) is a palindrome.
904 has a cube that is the sum of 3 positive cubes.
905 is the smallest composite number that is not the sum of a prime and a power of 2.
906 is the number of perfect graphs with 7 vertices.
907 is the largest n so that Q(√n) has class number 3.
909 is a value of n that has has no digits in common with 2n, 3n, 4n, 5n, 6n, 7n, 8n, or 9n.
911 is the American emergency number.
912 is a Pentanacci number.
913 has exactly the same digits in 3 different bases.
914 is the number of binary rooted trees with 15 vertices.
916 is a strobogrammatic number.
917 is the only positive number known whose 9th power can be written as the sum of ten 9th powers.
918 is a number that does not have any digits in common with its cube.
919 is the smallest number which is not the difference between palindromes.
922 = 1234 in base 9.
923 multiplied by its successor gives a number concatenated with itself.
924 is the 6th central binomial coefficient.
925 is the number of partitions of 37 in which no part occurs only once.
927 is the 13th tribonacci number.
929 is a Proth prime.
930 is the number of even permutations on 7 elements with no fixed points.
934 has a 5th root that starts 3.25252225....
935 is a number whose sum of divisors is a 4th power.
936 is a pentagonal pyramidal number.
939 has a cube root whose decimal part starts with the digits 1-9 in some order.
940 is the maximum number of regions space can be divided into by 15 spheres.
941 is the smallest number which is the reverse of the sum of its proper substrings.
945 is the smallest odd abundant number.
946 is a hexagonal pyramidal number.
948 is the number of symmetric plane partitions of 24.
949 is the larger number in a Ruth-Aaron pair.
951 is the number of functions from 8 unlabeled points to themselves.
952 = 93 + 53 + 23 + 9 × 5 × 2.
953 is the largest prime factor of 54321.
956 is the number of multigraphs with 16 vertices and 4 edges.
957 is a value of n for which σ(n) = σ(n+1).
959 is a Carol number.
960 is the sum of its digits and the cube of its digits.
961 is a square whose digits can be rotated to give another square.
964 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in the center.
966 is the Stirling number of the second kind S(8,3).
967 is the number of 6-digit triangular numbers.
969 is a tetrahedral palindrome.
973 is the number of inequivalent asymmetric Ferrers graphs with 25 points.
974 is the number of multigraphs with 5 vertices and 10 edges.
976 has a square formed by inserting a block of digits inside itself.
977 is a Stern prime.
979 is the sum of the first 5 4th powers.
981 is the smallest number that has 5 different partitions into 3 parts with the same product.
982 is the number of partitions of 39 into distinct parts.
983 is a Wedderburn-Etherington number.
984 8 + 88 + 888.
985 is the 9th Pell number.
986 is a strobogrammatic number.
987 is the 16th Fibonacci number.
988 is the maximum number of regions a cube can be cut into with 18 cuts.
990 is a triangular number that is the product of 3 consecutive integers.
991 is a permutable prime.
992 is the number of differential structures on the 11-dimensional hypersphere.
993 is the number of paraffins with 8 carbon atoms.
994 is the smallest number with the property that its first 18 multiples contain the digit 9.
995 has a square formed by inserting a block of digits inside itself.
996 has a square formed by inserting a block of digits inside itself.
997 has a cube root that starts 9.98998998....
998 is the smallest number with the property that its first 55 multiples contain the digit 9.
999 is a Kaprekar number.
1000 = 103.
1001 is the smallest palindromic product of 3 consecutive primes.