## Monday, September 30, 2013

### 3032

3032 = 2 x 2 x 2 x 379.

3032 is the number of trees on 19 vertices with graph diameter 5.

3032 is the smallest positive number that can be written as sum of distinct Fibonacci numbers in 52 ways (A013583).

3032 is a number that is divisible by 8 and the difference between two cubes in at least one way (A038850).

3032 is a multiple of 8 with a digit sum of 8 (A069543).

The sum of the cubes of the digits of 3032 is equal to the sum of the digits of the cube of 3032 (A165551): 30323 = 27,873,248,768; 2 + 7 + 8 + 7 + 3 + 2 + 4 + 8 + 7 + 6 + 8 = 62 and 33 + 03 + 33 + 23 = 62.

## Friday, September 27, 2013

### 836

836 = 2 x 2 x 11 x 19.

836 is a weird number (abundant but not pseudoperfect) (A006037).

836 is a 17-gonal (or heptadecagonal) number: (A051869).

836 is a divisor of 453 - 1.

836 is the number of regions made by diagonals in a regular 38-gon that are heptagons (A067154).

836 (a non-palindrome) has a palindromic square (A002778): 8362 = 698896.

621,770 + 77,126 = 8362 = 698896 and 621,770 - 77,126 = 7382 = 544,644.

836 is the numerical equivalent of TEN on a touch-tone telephone.

Source: Number Gossip

## Thursday, September 26, 2013

### 1200

1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5.

1200 is 3333 in base 7. It is 363 in base 19.

1200 is the sum of a twin prime pair (A054735): 1200 = 599 + 601.

1200 is a concentric dodecagonal number (A195143).

1200 is the number of regions made by diagonals in a regular 48-gon that are heptagons (A067154).

1200 is a number that can be expressed as the difference of squares of primes in just three distinct ways (A090782).

1200 is a divisor of 492 - 1.

## Wednesday, September 25, 2013

### 2526

2526 = 2 x 3 x 421.

2522, 2523, 2524, 2525, 2526, and 2527 are six consecutive numbers that are all the product of exactly three primes.

2526 is 666 in base 20 (A121205).

2526 is the concatenation of two consecutive increasing numbers (A127421).

2526 is a number for which the product of its digits (120) is 8 times the sum of its digits (15) (A062040).

2526 is the sum of nine distinct pentatope numbers (A104399).

## Tuesday, September 24, 2013

### 3046

3046 = 2 x 1523.

3046 is the product of two primes whose difference is a perfect square (A143416): 1523 - 2 = 1521 =  392.

3046 is 11611 in base 7 (A043015 and A043400).

3046 is a centered heptagonal number (A069099).

3046 is a number n such that n2 is palidromic in base 3 (122110101011221) (A029984).

3046 is the sum of the first 23 isolated (single or non-twin) primes (A153478).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, September 23, 2013

### 3604

3604 = 2 x 2 x 17 x 53.

3604 and its reversal (4063) are each multiples of 17 (A062906 and A062915).

3604 has two representations as a sum of two squares: 3604 = 22 + 602 = 302 + 522.

3604 is a divisor of 838 - 1.

3604 is 11221111 in base 3. It is 103404 in base 4 and 24404 in base 5. It is 2104 in base 12 and 1104 in base 15.

3604 is the number of ways to cover (without overlapping) a ring lattice (necklace) of 36 sites with molecules that are 7 sites wide (A058366).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, September 20, 2013

### 5540

5540 = 2 x 2 x 5 x 277.

5540 has two representations as a sum of two squares: 5540 = 82 + 742 = 382 + 642.

5540 is the number of walks within N3 (the first octant of Z3) starting at (0, 0, 0) and consisting of 8 steps taken from {(-1, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)} (A148966).

3090972 = 95540955409 (A116501).

Both 5540 and the 5540th prime (54443) have non-increasing digits (A116067).

The Lego 5540 kit is for a Formula 1 racer.

5540 Smirnova is an asteroid discovered in 1971.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, September 19, 2013

### 798

798 = 2 x 3 x 7 x 19.

798 has the representation 798 = 36 + 69.

798 is a divisor of 116 - 1.

798 is 666 in base 11. It is 383 in base 15.

798 is the number of ternary square-free words of length 16.

798 is the smallest even number with digit sum 24 (A069532). The sum of the digits is equal to eight times the number of digits (A061425).

798 is the smallest positive even integer that is an unordered sum of two primes in exactly 38 ways (A023036).

## Wednesday, September 18, 2013

### 854

854 = 2 x 7 x 61.

854 is the largest number that together with its square (729,316) uses different digits not more than once (A059930).

854 is the smallest number n such that it is the sum of two positive cubes (854 = 53 + 93) and n + 1 (855) is also the sum of two positive cubes (A003325 and A024670).

854 are the first three digits of the 27th Mersenne prime (A138864).

854 is 707 in base 11.

854 is the sum of six positive cubes in exactly three ways (A048931).

Source: Number Gossip

## Tuesday, September 17, 2013

### 579

579 = 3 x 193.

579, 581, and 583 are three consecutive odd numbers that are all semiprimes (A092207).

579 is the sum of the squares of three consecutive primes (A133529): 579 = 112 + 132 + 172.

579 is a menage number (A000179).

579 is 2403 in base 6 and 403 in base 12. It is 21003 in base 4 and 1103 in base 8.

579 is the number of graphs with 7 vertices that have chromatic number 3.

579 is a structured great rhombicosidodecahedral number (A100145).

## Monday, September 16, 2013

### 696

696 = 2 x 2 x 2 x 3 x 29.

696 is a palindrome n so that n(n + 8) is also palindromic (489984).

696 has the representation 36 - 33.

970,225 is the fourth square number that is the sum of the square of two consecutive numbers (696 and 697): 970,225 = 9852 = 6962 + 6972. In other words, (696, 697, 985) is the fourth Pythagorean triple where two sides are consecutive integers.

696 is 3120 in base 6 and 2013 in base 7. It is 853 in base 9 and 583 in base 11.

696 is the sum of eight consecutive primes: 696 = 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103.

## Friday, September 13, 2013

### 8450

8450 = 2 x 5 x 5 x 13 x 13.

8450 is 20402 in base 8.

8450 has five representations as a sum of two squares: 8450 = 132 + 912 = 232 + 892 = 352 + 852 = 472 + 792 = 652 + 652.

8450 is a divisor of 994 - 1.

84502 can be written as a sum of two squares in 12 ways. In other words, 8450 is the hypotenuse of exactly 12 distinct integer-sided right triangles.

8450 is the maximum number of regions into which the plane can be divided using 33 concave quadrilaterals (A077591).

8450 is the number of basic blocks of size 5 x 14 for tilings with square tiles of size up to 5 x 5 (A054858).

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, September 12, 2013

### 893

893 = 19 x 47.

893 is a semiprime that is the product of two distinct non-Sophie Germain primes (A157345).

893 is a divisor of 466 - 1.

893 has a square whose digits each occur twice (A052049): 8932 = 797449.

893 is 1020002 in base 3 and 1202 in base 9 (A037314).

893 is the sum of 12 positive fifth powers (A003357).

893 is the sum of six positive cubes in exactly three ways (A048931).

## Wednesday, September 11, 2013

### 2311

2311 is a prime number.

2309 and 2311 form a twin prime pair.

2311 is the largest member in a set of twin primes generated by the formula 30(n*(n + 5)/2) + 60 +1 and - 1, for n = 1 to 10.

2311 is the concatenation of the first three prime Ulam numbers (2, 3, 11).

2311 is a Euclid number.

2311 is 4407 in base 8 and 1407 in base 12. It is 907 in base 16 and 727 in base 18.

2311 is a divisor of 4122 - 1.

November 23 is the only date that can be read as a prime in both formats: "day-month" (2311) or "month-day" (1123).

Source: Prime Curios!

## Tuesday, September 10, 2013

### 571

571 is a prime number.

569 and 571 form a twin prime pair.

571 is a centered triangular number.

571 is the index of a prime Fibonacci number.

571 is 4241 in base 5. It is 1444 in base 7.

571 is a divisor of 9010 - 1.

U-571 is a 2000 film about a World War II German submarine captured by a disguised U.S. submarine.

The USS Nautilus (SSN-571) was the world's first operational nuclear-powered submarine.

Source: Prime Curios!

## Monday, September 9, 2013

### 712

712 = 2 x 2 x 2 x 89.

712 is the sum of the first 21 primes (A007504 and A073619).

712 is the largest number known that does not have any digits in common with its 8th power (66,045,000,696,445,844,586,496).

712 is the sum of 11 positive 5th powers (A003356).

712 has a representation as a sum of two squares: 712 = 62 + 262.

712 is a divisor of 554 - 1.

## Friday, September 6, 2013

### 827

827 is a prime number.

827 and 829 form a twin prime pair.

827 is the smallest prime formed from the concatenation of two consecutive cubes.

827 is the sum of seven consecutive primes: 827 = 103 + 107 + 109 + 113 + 127 + 131 + 137.

There are 827 Ulam numbers below 10,000.

827 is the number of asymmetric trees with 11 vertices.

827 is a divisor of 2014 - 1.

The unabridged Running Press edition of Gray's Anatomy contains 827 illustrations.

Source: Prime Curios!

## Thursday, September 5, 2013

### 3624

3624 = 2 x 2 x 2 x 3 x 151.

3624 is a number divisible by each of its digits (A187238).

3624 is the smallest number that starts off a sequence of four consecutive numbers with at least four prime divisors each.

3624 is the first of five consecutive squareful (nonsquarefree) numbers (A070284 and A078144).

3624 is the sum of the first 34 palindromes (A046489).

3624 is a number n such that 25n + 1 is a square (A219259).

3624 is the number of primes between 59 and 510 (A062517).

3624 is a divisor of 1910 - 1.

Source: Number Gossip

## Wednesday, September 4, 2013

### 895

895 = 5 x 179.

895 is a Woodall number. It has the form 2n n - 1 for n = 7 (A003261).

895 is a Smith number (A006753). The sum of the digits of 895 equals the sum of the digits of its prime factors. It is also the smallest multiple of five with a digit sum of 22 (A069534).

895 is a number that has no more than one zero in its binary representation (A089633 and A030130): 1101111111.

895 and the 895th prime (6967) have only the digit 9 in common (A107940).

Every base 5 digit of 895 (12040) is a base 9 digit of 895 (1204) (A037396).

## Tuesday, September 3, 2013

### 775

775 = 5 x 5 x 31.

775 is the smallest number whose ninth power has 26 digits.

775 is 1100000111 in base 2 and 11100 in base 5 (A033042). It is 30013 in base 4 and 3331 in base 6.

775 is a hypotenuse for which there exist two distinct integer triangles (A084646).

775 is a number n such that n and n2 (600625) have the same integer sum (19).

775 is the sum of five consecutive cubes (A217843): 775 = 33 + 43 + 53 + 63 + 73.