## Tuesday, September 30, 2014

### 9900

9900 = 2 x 2 x 3 x 3 x 5 x 5 x 11.

9900 is a pronic number, the product of two consecutive integers: 9900 = 99 x 100.

9900 has two distinct digits in base 2 (10011010101100), base 10 (9900), base 19 (1881), and base 21 (1199), each using two digits the same number of times.

9900 divides 1910 - 1.

Source: Number Gossip

## Monday, September 29, 2014

### 4459

4459 = 7 x 7 x 7 x 13.

4459 divides 1812 - 1.

4459 is a number having exactly four representations by the quadratic form x2 + xy + y2 with 0 less than or equal to x less than or equal to y (A198775).

4459 is the number of Ramanujan primes less than 100,000 (A181671).

Source: OEIS

## Friday, September 26, 2014

### 5873

5873 = 7 x 839.

5873 divides 11 + 22 + 33 + . . . + 58735873 (A128981).

5873 is a number n such that n divides the sum of the first n numbers from Flavius Josephus's sieve (A218665).

## Thursday, September 25, 2014

### 1825

1825 = 5 x 5 x 73.

1825 is an octagonal number (A000567).

1825 is the smallest number whose square begins with three 3s (A131573 and A025286 and A025304 and A034982).

1825 has three representations as a sum of two squares (A025313): 1825 = 122 + 412 = 152 + 402 = 232 + 362.

1825 is the hypotenuse of two primitive Pythagorean triples: 18252 = 7672 + 16562 = 9842 + 15372.

1825 divides 742 - 1.

## Wednesday, September 24, 2014

### 4320

4320 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5.

4320 = (6 + 4) x (6 + 3) x (6 + 2) x (6 + 0).

4320 = 7! - 6! (A001563 and A058295).

4320 is the maximal kissing number of a 16-dimensional laminated lattice (A002336).

4320 is a number n such that n! is the product of exactly four smaller factorials (A109097).

4320 divides 538 - 1.

Source: OEIS

## Tuesday, September 23, 2014

### 5942

5942 = 2 x 2971.

5942 is the maximum number of regions the plane is divided into by 45 triangles (A077588).

5942 is the number of partitions of 51 in which the greatest part is 6 (A026812).

5942 divides 556 - 1.

Source: OEIS

## Monday, September 22, 2014

### 5545

5545 = 5 x 1109.

5545 is a member of the Fibonacci-type sequence starting with 1 and 5 (A022095).

5545 uses only the digits 1 and 2 in base 4 (1112221) and base 7 (22111).

5545 is a concentric dodecagonal number (A195143).

5545 has two representations as a sum of two squares: 5545 = 192 + 722 = 282 + 692.

5545 is the hypotenuse of two primitive Pythagorean triples: 55452 = 27362 + 48232 = 38642 + 39772.

## Friday, September 19, 2014

### 5276

5276 = 2 x 2 x 1319.

5276 is the number of binary strings of length 14 with no substrings equal to 0000 or 0010 (A164387).

5276 is a number n such that n - 3, n + 3, and n + 5 are all primes (A144842).

5276 is the number of moves needed to solve the 4-peg Tower of Hanoi puzzle with 22 disks (A160002).

5276 cannot be written as a sum of three squares.

Source: OEIS

## Thursday, September 18, 2014

### 1796

1796 =  2 x 2 x 449.

1796 is the palindrome 2110112 in base 3 (A043002).

1796 is the number of lines through exactly 10 points of a 52 x 52 grid of points (A018817).

1796 is the sum of 11 nonzero 8th powers (A003389).

1796 has a representation as a sum of two squares: 1796 = 142 + 402.

1796 divides 674 - 1.

In the year 1796, Carl Friedrich Gauss proved that a regular 17-gon can be constructed using only compass and straightedge.

Source: OEIS

## Wednesday, September 17, 2014

### 3810

3810 = 2 x 3 x 5 x 127.

3810 is the number of ways to place a non-attacking white and black pawn on a 9 x 9 chessboard (A035290).

3810 is a sum of primes between successive pairs of twin primes (A078731).

3810 in base 6 and base 9 both use the same set of digits {0, 2, 3, 5} (A037436).

3810 divides 196 - 1.

## Tuesday, September 16, 2014

### 9931

9931 is a prime number.

9929 and 9931 form a twin prime pair. 9931 is the larger of the greatest twin prime pair with four digits (A114429).

9931 and its reversal, 1399, are both primes (A101782).

9931 is a prime with 10 as the smallest positive primitive root (A061323).

9931 is a prime p such that p - 2 and p3 - 2 are also prime (A240124).

9931 is a prime that is the sum of 8 but no fewer squared primes (A183216).

Source: OEIS

## Monday, September 15, 2014

### 5992

5992 = 2 x 2 x 2 x 7 x 107.

5992 is the number of binary strings of length 13 with equal numbers of 00101 and 10010 substrings (A164247).

5992 is the number of powerful numbers not exceeding 223 (A062762).

5992 is 43424 in base 6.

Source: OEIS

## Friday, September 12, 2014

### 9147

9147 = 3 x 3049.

9147 is 6966 in base 11.

9147 is the number of primitive (aperiodic) reversible strings with 9 beads using exactly three different colors (A056319).

9147 is the sum of the first 45 primes of the form 4a - 1 (A038347).

Source: OEIS

## Thursday, September 11, 2014

### 6233

6233 = 23 x 271.

6233 is the least number that can be expressed as the sum of a prime number and a nonzero square in just 28 ways (A064283).

6233 is 22112212 in base 3. It is 144413 in base 5 and 14131 in base 8. 6233 is 8485 in base 9.

6233, 623, 62, and 6 are all semiprimes (A085733).

6233 is the number of primes of the form x2 + 1 less than 233 (A083847).

Source: OEIS

## Wednesday, September 10, 2014

### 1793

1793 = 11 x 163.

1793, 1795, 1797. and 1799 are all semiprimes (A092126).

1793 is a pentanacci number (A001591).

1793 is the sum of three distinct cubes in two or more ways (A024974).

1793 is the number of tilings of a 2 x 8 board wth 1 x 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares) (A127864).

1793 is a number such that its digit sum in base 2 and its digit sum in base 10 is in the ratio of 2:10 (A135110).

1793 divides 5815 - 1.

## Tuesday, September 9, 2014

### 5453

5453 = 7 x 19 x 41.

5453 is a potential magic constant of a 7 x 7 magic square composed of consecutive primes (A188536).

5453 is a number such that the number of 3s in base 5 is 4 (A043364): 133303.

5453 divides 836 - 1.

Source: OEIS

## Monday, September 8, 2014

### 1590

1590 = 2 x 3 x 5 x 53.

1590 is 818 in base 14 and 636 in base 16.

1590 is a heptadecagonal number (A051869).

1590 is a number n such that 2n + 1, 4n + 1, and 8n+ 1 are all primes (A124041).

1590 is the sum of eight nonzero 6th powers (A003364).

1590 divides 234 - 1.

Source: OEIS

## Friday, September 5, 2014

### 4220

4220 = 2 x 5 x 211.

4220 is a number n for which the sum of the first n composite numbers is a palindrome (A053779).

4220 is the maximum number of regions the plane is divided into by 38 triangles (A077588).

4220 is the number of binary rooted trees with 39 nodes and internal path length 39 (A108643).

4220 divides 7110 - 1.

## Thursday, September 4, 2014

### 5940

5940 = 2 x 2 x 3 x 3 x 3 x 5 x 11.

5940 is divisible by its reverse, 495 (A223080).

5940 = (9 x 10 x 11 x 12)/2 (A033486).

5940 is 2244 in base 14 (A035012).

5940 is the sum of the interior angles (in degrees) of a 35-sided polygon (A066164).

5940 divides 896 - 1.

## Wednesday, September 3, 2014

### 4546

4546 = 2 x 2273.

The number 4546 and its prime factors use each of the digits from 2 to 7 (A058760).

4546 is a member of the sequence in which each term is the sum of the previous term and the square of the term before that (A000278).

4546 has a representation as a sum of two squares: 4546 = 392 + 552.

Source: OEIS

## Tuesday, September 2, 2014

### 2708

2708 = 2 x 2 x 677.

2708 in base 6 has digits in the order 2, 0, 3, 1, then repeats 2 (A037725).

2708 in base 2 has exactly 10 runs (A043577): 101010010100.

2708 is a number n such that the three numbers n - 1, n + 3, and n + 5 are all prime (A144840).

2708 has a representation as a sum of two squares: 2708 = 22 + 522.

2708 is the number of partitions of 84 into distinct parts, where the difference between the number of odd parts and the number of even parts is 5 (A240141).

Source: OEIS