## Monday, June 30, 2014

### 5110

5110 = 2 x 5 x 7 x 73.

5110 is a multiple of 7 whose digit sum is 7 (A063416).

5110 and the square of 5110 use only the digits 0, 1, 2, 5, and 6 (A136823).

5110 is the number of nonalternating knots with 13 crossings (A051763).

5110 is 21000021 in base 3. It is 7007 in base 9 (A043034).

5110 divides 813 - 1.

Source: OEIS

## Friday, June 27, 2014

### 9327

9327 = 3 x 3109.

9327 is a value of n for which n and 2n together use each digit 1 to 9 exactly once (A064160).

9327 is a number n such that 2n + 9 is prime (A057196).

9327 is a number that cannot be written as a sum of three squares.

9327 divides 8521 - 1.

## Thursday, June 26, 2014

### 9317

9317 = 7 x 11 x 11 x 11.

9317 is a number n having two distinct prime factors p, q with q = p + 4 (A143203 and A195106).

9317 is a number n with the property that the largest proper divisor of n is a cube (A187104).

9317 is the number of standard Young tableaux with 11 cells and exactly one succession (A238126).

9317 is a number n such that n ends with 7 and is the difference between two cubes in at least one way (A038862).

Source: OEIS

## Wednesday, June 25, 2014

### 8811

8811 = 3 x 3 x 11 x 89.

8811 is a multiple of 11 containing 11 in its decimal representation (A121031).

8811 is the number of 12 x 12 binary arrays symmetric under horizontal reflection with all ones connected only in a one by five or five by one block (A145065).

8811 divides 3412 - 1.

Source: OEIS

## Tuesday, June 24, 2014

### 6395

6395 = 5 x 1279.

6395 is the number of ways to divide a 12 x 12 grid of points into two sets using a straight line (A114043).

6395 is the number of primes of the form 1 + b4 for b less than 105 (A215048).

6395 is the number of connected functions on 9 points with a single labeled point (A038002).

## Monday, June 23, 2014

### 9908

9908 = 2 x 2 x 2477.

9908 is the number of times the digit 2 appears in the first 105 (100,000) digits of pi (A099293).

9908 is the least number that can be expressed as the sum of a prime number and a nonzero square in just 36 different ways (A064283).

9908 is the number of fixed polyominoes with 9 cells (A006762).

9908 is the number of placements of brackets in a monomial of degree 9 in an algebra with two commutative multiplications (A226909).

9908 has a representation as a sum of two squares: 9908 = 382 + 922.

9908 is 304113 in base 5 and 113512 in base 6.

Source: OEIS

## Friday, June 20, 2014

### 2888

2888 = 2 x 2 x 2 x 19 x 19.

2888 is 21212 in base 6.

2888 is the first of five consecutive squareful numbers.

2888 is the smaller of two consecutive numbers divisible by cubes (A068140).

2888 is the smallest multiple of 8 with a digit sum of 26 (A069536).

2888 has a representation as a sum of two identical squares (A001105): 2888 = 382 + 382.

2888 divides 696 - 1.

## Thursday, June 19, 2014

### 5247

5247 = 3 x 3 x 11 x 53.

5247 is the number of ordered ways to write 1 as a sum of reciprocals of integers no larger than 10.

5247 has three 1s and three 3s in its base 4 representation (A045127).

5247 divides 2312 - 1.

5247 is a number that cannot be written as a sum of three squares.

## Wednesday, June 18, 2014

### 8396

8396 = 2 x 2 x 2099.

8396 does not occur in its factorial in base 2 (binary notation) (A093685).

8396 is a number such that it has four 3s in its base 7 representation (A043408).

8396 has four 0s and two 3s in its base 4 representation (A045083).

8396 is the number of 4-bead necklaces labeled with numbers -46 . . . 46 not allowing reversal, with sum zero and first and second differences in -46 . . . 46 (A209008).

## Tuesday, June 17, 2014

### 1950

1950 = 2 x 3 x 5 x 5 x 13.

1950 = (144 + 145 + . . . + 156) = (157 + 158 + . . . + 168) (A059270).

1950 is 132132 in base 4, 5454 in base 7, and 3636 in base 8. It is 1166 in base 12 (A033010).

1950 is a number n such that the square of n is the sum of four consecutive primes (A051395).

1950 divides 496 - 1.

1950 is a year with exactly two "Friday the 13ths" (A190652).

## Monday, June 16, 2014

### 1933

1933 is a prime number.

1931 and 1933 form a twin prime pair.

1933 is centered heptagonal number (A069099).

1933 = (19 + 28 + 37 + 46 + 55)/5.

1933 has a representation as the sum of two squares: 1933 = 132 + 422.

1933 is the hypotenuse of a primitive Pythagorean triple: 19332 = 10922 + 15952.

1933 divides 1021 - 1.

Source: Prime Curios!

## Friday, June 13, 2014

### 3626

3626 = 2 x 7 x 7 x 37.

3626 is 24442 in base 6.

3626 is the smallest nonnegative number that is the sum of three squares in exactly 23 ways (A000437).

3626 is a member of the Fibonacci-like sequence beginning with 1 and 9 (A022099).

3626 is the center element of a series of five successive non-squarefree numbers (A188296).

3626 has a representation as a sum of two squares: 3626 = 352 + 492.

3626 divides 3112 - 1.

## Thursday, June 12, 2014

### 5582

5582 = 2 x 2791.

The sum of the digits of 5582 is the square root of the product of the digits of 5582 (A117720).

5582 is contained as a substring in the 5582nd triangular number (A119238).

5582 is the number of distinct connected monocyclic bipartite graphs with 13 vertices (A214650).

5582 divides 913 - 1.

Source: OEIS

## Wednesday, June 11, 2014

### 3442

3442 = 2 x 1721.

3442 is a semiprime with a prime sum of decimal digits and a prime sum of prime factors (A108610).

3442 is exactly between the nearest square and the nearest triangular number (A233074).

3442 is the number of three-dimensional polyominoes with 8 cells (A006766).

3442 has a representation as a sum of two squares: 3442 = 292 + 512.

Source: OEIS

## Tuesday, June 10, 2014

### 1911

1911 = 3 x 7 x 7 x 13.

1911 is 11101110111 in base 2 (binary) (A023691), 131313 in base 4 (A037576), and 1133 in base 12 (A033010). It is 876 in base 15 and 777 in base 16 (A033029).

1911 is a hendecadonal number (A051682). It is also a heptagonal pyramidal number (A002413).

1911 divides 793 - 1.

1911 was a year with exactly two "Friday the 13ths" (A190652).

## Monday, June 9, 2014

### 2637

2637 = 3 x 3 x 293.

2637 is 5115 in base 8.

Deleting the middle two digits of 2637 produces a cube (A217297).

2637 is the number of commutative monoids of order 7 (A058131).

2637 is the sum of nine distinct pentatope numbers (A104399).

2637 has a representation as a sum of two squares: 2637 = 62 + 512.

## Friday, June 6, 2014

### 5314

5314 = 2 x 2657.

5314 is a semiprime with a prime sum of decimal digits and a prime sum of prime factors (A108610).

5314 is the sum of three consecutive hexagonal numbers (A129109).

5314 has a representation as a sum of two squares: 5314 = 332 + 652.

5314 is the number of positive integers that are not the sum of distinct 40th-order polygonal numbers (A025524).

5314 is a centered 21-gonal number (A069178).

Source: OEIS

## Thursday, June 5, 2014

### 9347

9347 = 13 x 719.

9347 is a value of n for which the sum of the square-free divisors of n and n + 1 are the same (A063964).

9347 is a number n such that googol - n is a prime (A108251).

9347 is the number of primes between 46 and 463 (A117491).

## Wednesday, June 4, 2014

### 1902

1902 = 2 x 3 x 317.

1902 has cube that contains only even digits (A052004).

1902 is a number n such that 2n - 1, 4n - 1, and 6n - 1 are primes (A124486).

1902 is the sum of three consecutive semiprimes (A173968).

1902 is the number of primes p such that 8! - p is prime (A140088).

1902 is a year with exactly one "Friday the 13th" (A190651).

## Tuesday, June 3, 2014

### 1898

1898 = 2 x 13 x 73.

1898 is 1122 in base 12 (A033010). It is 868 in base 15.

1898 is the smallest multiple of 26 whose digits sum to 26 (A002998).

1898 is the number of primes between 262 and 263 (A079648).

1898 is the least positive integer that can be represented as the sum of a semiprime and a square in exactly 25 ways (A101181).

1898 has two representations as a sum of two squares: 1898 = 72 + 432 = 232 + 372. It is the sum of two squared primes in exactly two ways (A226539).

1898 divides 813 - 1.

Source: OEIS

## Monday, June 2, 2014

### 3255

3255 = 3 x 5 x 7 x 31.

3255 is 101010 in base 5 (A033042 and A033115). It is 23023 in base 6. 3255 uses only the digits 0, 1, 2, and 3 in every base up to and including base 7.

3255 is a number that is not the sum of a triangular number, a cube, and a Fibonacci number (A115177).

3255 is a number n such that n - 4, n - 2, n + 2, and n + 4 are prime (A173037).

3255 divides 924 - 1.

Source: OEIS