## Friday, March 30, 2012

### 3488

3488 = 2 x 2 x 2 x 2 x 2 x 109.

3488 has a fifth root that starts 5.11111. . .

3488 is the number of complete squares that fit inside a circle of radius 34, drawn on squared paper (A119677).

3488 is the number of sums payable using exactly 37 banknotes of denominations 1, 5, 10, 20, 50, 100 (change allowable) (A135526).

3488 has a representation as a sum of two squares: 3488 = 282 + 522.

3488 is a divisor of 334 - 1.

Source: What's Special About This Number?

## Thursday, March 29, 2012

### 3480

3480 = 2 x 2 x 2 x 3 x 5 x 29.

3480 is a Perrin number (A001608).

3480 is 110110011000 in base 2 (binary). It is 2020 in base 12.

3480 is an octagonal pyramidal number (A002414).

3480 is the number of ways to place two nonattacking queens on an 10 x 10 board (A036464).

Source: What's Special About This Number?

## Wednesday, March 28, 2012

### 361

361 = 19 x 19.

361 is a centered triangular number (A005448). It is also a centered octagonal number (A016754) and a centered decagonal number (A062786).

The representations of 361 in bases 2, 3, 4, 5, 6, 8, 9, and 10 all end in 1. It is 551 in base 8 and 441 in base 9. It is 121 in base 18.

361 is a square that remains a square when the last digits is removed (A023110).

361 and 3612 (130321) have the same digit sum (A058369): 3 + 6 + 1 = 10 = 1 + 3 + 0 + 3 + 2 + 1.

The game of Go is played on a grid of 19 x 19 lines, which produces 361 intersections on the game board.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, March 27, 2012

### 841

841 = 29 x 29.

841 is a centered square number. It is also a centered heptagonal number and a centered octagonal number.

841 has a representation as a sum of two squares: 841 = 202 + 212. It is the sum of two consecutive squares.

841 is the hypotenuse of a primitive Pythagorean triple: 8412 = 412 + 8402.

841 is the smallest 3-digit square whose digits are decreasing.

841 is the smallest binary prime square. It's a perfect square whose binary representation (1101001001) considered as a decimal is a prime number.

841 is a divisor of 414 - 1.

Source: Number Gossip

## Monday, March 26, 2012

### 935

935 = 5 x 11 x 17.

935 is a Lucas-Carmichael number (A006972).

The sum of the divisors of 935 is a square (A006532) and a fourth power (A019422): 1 + 5 + 11 + 17 + 55 + 85 + 187 + 935 = 1296 = 362 = 64.

935 is the sum of positive powers of its digits: 935 = 93 + 34 + 53 (A007532).

The sum of the digits of 935 is the largest prime factor of 935 (A052021): 9 + 3 + 5 = 17.

Source: What's Special About This Number?

## Friday, March 23, 2012

### 277

277 is a prime number.

76729 is the square of the prime 277 and the smallest square with five or more digits that is the concatenation of three primes (7, 67, and 29).

277 is the smaller prime factor of the semiprime 9000007, the first composite number of the series 97, 907, 9007, and so on.

277 has a representation as a sum of two squares: 277 = 92 + 142.

277 is the hypotenuse of a primitive Pythagorean triple: 2772 = 1152 + 2522.

The digit sum of 277 is a fourth power: 2 + 7 + 7 = 16 = 24.

277 = (2 + 7)2 + (7 + 7)2.

Source: Prime Curios!

## Thursday, March 22, 2012

### 170

170 = 2 x 5 x 17.

170 is 10101010 in base 2 (binary). It is 2222 in base 4.

170 has two representations as a sum of two squares: 170 = 12 + 132 = 72 + 112.

170 is the smallest number that can be written as the sum of the squares of two distinct primes, where each of these primes is the square of a prime added to another prime: 170 = (22 + 3)2 + (32 + 2)2.

170 is the start of a record-breaking run of consecutive integers (170 to 176) with an odd number of prime factors.

Each internal angle of a regular 36-sided polygon is 170 degrees.

Source: Prime Curios!

## Wednesday, March 21, 2012

### 926

926 = 2 x 463.

926 is the smallest number that cannot be formed using each of the digits 1 to 6 at most once, with the operators +, -, x, /, and ^.

The digits 926 appear two places after the digits 3.14 in the numbers eπ = 23.14069263. . . and π = 3.141592653. . . .

926 is 222 in base 21.

926 is the sum of six consecutive primes: 926 = 139 + 149 + 151 + 157 + 163 + 167.

Source: What's Special About This Number?

## Tuesday, March 20, 2012

### 427

427 = 7 x 61.

427 has a unique representation as a sum of three squares: 427 = 92 + 112 + 152.

427 is a value of n for which n! + 1 is a prime (A002981).

427 is 110101011 in base 2 (binary) (A006995) and 1551 in base 6.

427 is the solution to the postage stamp problem for 4 denominations and 10 stamps (A001209).

Source: What's Special About This Number?

## Monday, March 19, 2012

### 919

919 is a prime number.

919 is the 18th centered hexagonal number (hex number).

919 is the smallest palindromic number whose sum of digits (19) shows up as a substring of the number.

919 is the smaller number in the smallest pair of prime numbers that are mutually the sums of the same powers of each other's digits: 919 = 13 + 43 + 53 + 93 and 1459 = 93 + 13 + 93.

919 is the largest known palindromic prime for which the next prime (929) is also palindromic.

919 is the smallest palindromic prime equal to the difference of consecutive cubes:919 = 183 - 173.

Source: Prime Curios!

## Friday, March 16, 2012

### 1287

1287 = 3 x 3 x 11 x 13.

1287 is the binomial coefficient C(13,5) (A000389).

1287 is a divisor of 1003 - 1.

1287 is the smallest value that when multiplied by 7 has only the digits 0 and 91287 x 7 = 9009 (A096688).

A famously long sentence in Absalom, Absalom! by William Faulkner contains 1,287 words.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, March 15, 2012

### 1177

1177 = 11 x 107.

1177 is a heptagonal number.

1177 is the maximum number of regions into which 48 lines divide the plane.

1177 is a number whose sum of divisors is a fourth power: 1 + 11 + 107 + 1177 = 1296 = 64.

1177 is 414 in base 17.

Source: What's Special About This Number?

## Wednesday, March 14, 2012

### 1041

1041 = 3 x 347.

1041 is 13131 in base 5 and 545 in base 14.

1041, 1042, and 1043 are each semiprimes (the product of two primes) (A056809). 1041 is also the smallest of three consecutive squarefree numbers (A073251).

The sum of the digits of the product of the factorial of the digits of 1041 (1! x 0! x 4! x 1! = 24) is equal to the sum of the digits of 1041 (A082939): 1 + 0 + 4 + 1 = 6 = 2 + 4.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, March 13, 2012

### 310

310 = 2 x 5 x 31.

310 is 1234 in base 6. It is 262 in base 11.

310 is one of six numbers that when squared use the same digits: 3102 = 16900, 1402 = 19600, 3102 = 96100, 1032 = 10609, 2472 = 61009, and 3012 = 90601.

310 is the sum of six positive 5th powers (A003351): 310 = 35 + 25 + 25 + 15 + 15 + 15.

The sum of the digits of 310 is a square: 3 + 1 + 0 = 4 = 22.

Source: Positive Integers

## Monday, March 12, 2012

### 804

804 = 2 x 2 x 3 x 67.

804 is a 14-gonal (tetradecagonal) number (A051866).

Each of 804, 805, and 806 has three distinct prime factors (A140077).

804 is the number of linear arrangements of four blue, four red, and four green items such that there are no adjacent items of the same color (first and last elements considered as adjacent) (A110707).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, March 9, 2012

### 113

113 is a prime number. It is a Sophie Germain prime because 2 x 113 + 1 = 227 is also a prime.

113 is the smallest three-digit prime whose product and sum of digits is prime: 1 x 1 x 3 = 3 and 1 + 1 + 3 = 5.

113 has a representation as a sum of two squares: 113 = 72 + 82 (the sum of two consecutive squares).

113 is the hypotenuse of a primitive Pythagorean triple: 1132 = 152 + 1122.

113 is a centered square number.

1132 = 12769 and its reversal 96721 = 3112.

A113 is the license plate number of Andy's mom's vehicle in the film Toy Story.

Source: Number Gossip and Prime Curios!

## Thursday, March 8, 2012

### 865

865 = 5 x 173.

865 has two representations as a sum of two squares: 865 = 92 + 282 = 172 + 242.

865 is the hypotenuse of two primitive Pythagorean triples: 8652 = 2872 + 8162 = 5042 + 7032.

865 is 717 in base 11 and 151 in base 27.

865 is the sum of distinct factorials (A059590): 865 = 6! + 5! + 4! + 1!

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, March 7, 2012

### 386

386 = 2 x 193.

386 has a representation as a sum of two squares: 386 = 52 + 192.

386 is a centered heptagonal number.

386 is the number of regions into which the complex plane is cut by drawing lines between all pairs of 11th roots of unity.

386 is 282 in base 12.

Source: What's Special About This Number?

## Tuesday, March 6, 2012

### 958

958 = 2 x 479.

958 is the number of 3-colorable graphs with 5 vertices (A084279).

958 is a Smith number (A006753); the sum of its digits equals the sum of the digits of its prime factors: 9 + 5 + 8 = 2 + 4 + 7 + 9 = 22.

9582 = 917764 and 9592 = 919681 have the same digit sum (A202089): 34.

Source: What's Special About This Number?

## Monday, March 5, 2012

### 749

749 = 7 x 107.

749 is the number of ways to divide a 7 x 7 grid of points into two sets using a straight line.

The odd powers of 749 all end in 749, and its even powers end with 001.

749 is the sum of three consecutive primes: 749 = 241 + 251 + 257.

749 is the numerical equivalent of the word SIX on a touch-tone telephone.

Source: Number Gossip

## Friday, March 2, 2012

### 213

213 = 3 x 71.

The sum of the digits of 213 is the same as the product of its digits: 2 + 1 + 3 = 2 x 1 x 3 = 6.

213 is the number of perfect squared rectangles of order 13.

25,986 = 213 x 122 and (backwards) 312 x 221 = 68,952.

213 = 23 + 23 + 23 + 43 + 53.

213 was the apartment number of the infamous serial killer Jeffery Dahmer, and the title of a song by the thrash metal band Slayer.

Source: What's Special About This Number?

## Thursday, March 1, 2012

### 2177

2177 = 7 x 311.

2177 is 100010000001 in base 2 (binary) and 2222122 in base 3.

2177 is the number of permutations of length 10 within a distance 2 of a fixed permutation (A002524).

2177 is a centered 16-gonal number (A069129).

2177 is the sum of three but no fewer nonzero fourth powers: 2177 = 64 + 54 + 44 (A047714).

A transit of Mercury (as seen from Earth) is expected to take place in the year 2177 (A171466).

Source: On-Line Encyclopedia of Integer Sequences