## Wednesday, December 24, 2014

### 2015

2015 = 5 x 13 x 31.

2015 is palindromic in base 2 (binary): 11111011111 (A030130 and A168355). 2015 repeats the string 133 in base 4: 133133 (A020332). It repeats the string 37 in base 8: 3737 (A020336).

2015 is a Lucas-Carmichael number (A006972 and A129868).

2014, 2015, and 2016 each have three distinct prime factors (sphenic numbers) (A168626).

2015 is the sum of 10 distinct powers of 2 (A038461).

2015 is a number that cannot be written as a sum of three squares.

2015 divides 924 - 1.

2015 is a year with exactly three "Friday the 13ths" (A190653).

2015 is a year in which a blue moon occurs (a second full month to occur in a single calendar month) (A125680).

The year 2015 is the 100th anniversary of the founding of the Mathematical Association of America.

Source: OEIS

## Tuesday, December 23, 2014

### 6884

6884 = 2 x 2 x 1721.

6884 is the number of lines through at least two points of a 7 x 25 grid of points (A160847).

6884 has a representation as a sum of two squares: 6884 = 222 + 802.

Source: OEIS

## Monday, December 22, 2014

### 1853

1853= 17 x 109.

1853 is a semiprime divisible by the sum of its digits (A118693).

1853 is the sum of two positive cubes and divisible by 17 (A099178).

1853 is a number n such that the strings n9n and 9n9 are both primes (A090265).

1853 has two representations as a sum of two squares: 1853 = 22 + 432 = 222 + 372.

1853 is the hypotenuse of two primitive Pythagorean triples: 18532 = 1722 + 18452 = 8852 + 16282.

1853 divides 334 - 1.

Source: OEIS

## Friday, December 19, 2014

### 6881

6881 = 7 x 983. It is the product of two distinct primes (A006881).

6881 is a composite number not ending in 0 that yields a prime when turned upside down (A048889).

The absolute difference between two consecutive digits of 6881 in base 6 (51505) is greater than or equal to 4 (A032988).

Source: OEIS

## Thursday, December 18, 2014

### 7894

7894 = 2 x 3947.

7894 is a number n for which n and 8n together use each digit from 1 to 9 exactly once (A115932).

7894 is the number of isocent sequences of length 15 with exactly nine ascents (A243235).

## Wednesday, December 17, 2014

### 3740

3740 = 2 x 2 x 5 x 11 x 17.

3740 is the sum of consecutive squares in two ways (A062681).

3740 is 25152 in base 6 and 5115 in base 9.

3740 is the number of tatami tilings of a 3 x 10 grid (with monomers allowed) (A180970).

3740 divides 214 - 1.

## Tuesday, December 16, 2014

### 1834

1834 = 2 x 7 x 131.

1834 is an octahedral number (A005900).

1834 is the sum of the cubes of the first five primes (A098999).

1834 is a number that has more different digits than its square (A061277).

1834 is 3452 in base 8.

1834 divides 9913 - 1.

## Monday, December 15, 2014

### 7799

7799 = 11 x 709.

7799 is a semiprime made up of two rums of identical digits (A116063).

7799 is the least semiprime whose sum of prime factors equals 6! (A193216).

The sum of the digits of 7799 is 8 times the number of digits (A061425).

7799 divides 9620 - 1.

Source: OEIS

## Friday, December 12, 2014

### 6723

6723 = 3 x 3 x 3 x 3 x 83.

6723 is a value of n for which 3n and 8n together use each digit from 0 to 9 exactly once.

6723 is 25413 in base 7.

6723 is the solution to the postage stamp problem with 3 denominations and 47 stamps (A001208).

6723 is the maximum number of points visible from some point in a cubic 20 x 20 x 20 lattice (A141227).

## Thursday, December 11, 2014

### 6675

6675 = 3 x 5 x 5 x 89.

6675 is a composite number that is the sum of two, three, four, and five consecutive composite numbers (A151745).

6675 is a number n such that n and the square of n use only the digits 2, 4, 5, 6, and 7 (A137094).

6675 is 25314 in base 7.

6675 divides 3420 - 1.

Source: OEIS

## Wednesday, December 10, 2014

### 4351

4351 = 19 x 229.

The sum of the digits of 4351 is equal to the sum of the digits of its largest prime factor (A219340).

4351 is a centered decagonal number (A062786).

4351 is the concatenation of the 14th prime number and the 14th lucky number (A032603).

4351 divides 946 - 1.

4351 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Tuesday, December 9, 2014

### 4347

4347 = 3 x 3 x 3 x 7 x 23.

4347 is a heptagonal number (A000566). It is also a pentagonal number (A049452).

4347 is the concatenation of the 27th and 28th primes (A045533).

4347 is a value of n for which 2n and 5n together use each of the digits 1 to 9 exactly once.

4347 is the number of regions in a regular 63-gon that are octagons (A067155).

4347 divides 2218 - 1.

Source: Number Gossip

## Monday, December 8, 2014

### 5481

5481 = 3 x 3 x 3 x 7 x 29.

5481 is 1956 in base 15 and 1569 in base 16.

5481 is the average of four consecutive odd squares (A173960).

5481 divides 889 - 1.

Source: OEIS

## Friday, December 5, 2014

### 4100

4100 = 2 x 2 x 5 x 5 x 41.

4100 is 5555 in base 9. It is 12121212 in base 3 (A037480 and A162216).

4100 is a multiple of 5 with a digit sum of 5 (A069540).

4100 has three representations as a sum of two squares (A025286): 4100 = 22 + 642 = 162 + 622 = 402 + 502.

4100 divides 3110 - 1.

## Thursday, December 4, 2014

### 8242

8242 = 2 x 13 x 317.

Concatenating 8242 with 1 less than 8242 produces a square (A054214 and A054215): 82428241 = 90792.

The base 4 representation of 8242 has 4 zeroes, 2 twos, and no ones (A045033 and A045059): 2000302.

8242 has two representations as a sum of two squares: 8242 = 412 + 812 = 592 + 692.

## Wednesday, December 3, 2014

### 1821

1821 = 3 x 607.

1821 is a number that yields a prime whenever 1 is inserted anywhere in it, including at the beginning or end (A068679 and A216165).

1821 is a centered icosagonal number (A069133). It is also a concentric decagonal number (A195142).

1821 is the number of primes less than the cube of 25 (A038098).

1821 is 2111110 in base 3. It is 130131 in base 4 and 3435 in base 8. 1821 is 24241 in base 5.

Source: OEIS

## Tuesday, December 2, 2014

### 3500

3500 = 2 x 2 x 5 x 5 x 5 x 7.

3500 is a number that is the sum of two positive cubes and divisible by 7 (A101421) and divisible by 5 (A224485).

3500 is the sum of three nonnegative cubes in more than one way (A001239).

3500 is the number of rooted trees with 24 nodes with every leaf at height 3 (A048808).

3500 is a number n such that n and the square of n have only the digits 0, 1, 2, 3, and 5 in common (A136811).

3500 divides 574 - 1.

Source: OEIS

## Monday, December 1, 2014

### 3048

3048 = 2 x 2 x 2 x 3 x 127.

3048 is a number that can be expressed as the difference of the squares of primes in just two distinct ways (A090788).

3048 is a number divisible by each of its digits, excluding 0 (A187398).

3048 is a number n such that n and the nth prime have only the digit 4 in common (A107935).

The 3048th prime divides the 3048th Fibonacci number (A075702).

3048 divides 196 - 1.

Source: OEIS

## Wednesday, November 26, 2014

### 2445

2445 = 3 x 5 x 163.

2445 is a truncated tetrahedral number (A005906).

2445 is a number n such that n! has a square number of digits (A006488).

2445 is the sum of nine nonzero 6th powers (A003365).

2445 is a lucky number that is divisible by the sum of its digits (A118564).

2445 divides 596 - 1.

## Tuesday, November 25, 2014

### 1795

1795 = 5 x 359.

1795, 1797, and 1799 are consecutive semiprimes (A133609).

1795 is the product of two distinct safe primes (A157352).

1795 has a base 5 representation (24140) that begins with its base 9 representation (2414).

1795 is the sum of 10 nonzero 8th powers (A003388).

1795 is a Smith semiprime (A098837).

## Monday, November 24, 2014

### 1792

1792 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

1792 is a Friedman number (A036057).

1792 is the maximum number of pieces obtained by slicing a bagel (torus) with 21 cuts (A003600).

1792 is a composite number such that the square root of the sum of squares of its prime factors is an integer (A134605).

1792 is the number of simple graphs with 9 vertices and two cycles (A112410).

1792 divides 978 - 1.

Source: OEIS

## Friday, November 21, 2014

### 5101

5101 is a prime number.

5099 and 5101 form a twin prime pair.

5101 is the initial prime in a set of four consecutive primes with common difference 6 (A033451).

5101 is a prime formed from merging four successive digits in the decimal expansion of e (A104845).

5101 is a prime whose sum of digits is 7 (A062337).

5101 is a centered 17-gonal number (A069130).

5101 has a representation as a sum of two squares: 5101 = 502 + 512. 5101 is a prime that is the sum of at least two consecutive squares (A163251).

5101 is the hypotenuse of a primitive Pythagorean triple: 51012 = 1012 + 51002.

5101 divides 4620 - 1.

Source: OEIS

## Thursday, November 20, 2014

### 3001

3001 is a prime number.

2999 and 3001 form a twin prime pair.

3001 is a prime whose digit sum is 4 (A062339). It is the largest 4-digit prime with minimum digit sum (A069664).

3001 is a centered decagonal number (A062786).

3001 is a prime that can be expressed as the sum of distinct powers of 3 (A077717).

3001 is 1/24 of the 24th Fibonacci number.

3001 has a representation as a sum of two squares: 3001 = 202 + 512.

3001 is the hypotenuse of a primitive Pythagorean triple: 30012 = 20402 + 22012.

3001 divides 2015 - 1.

Arthur C. Clarke wrote a book titled 3001: The Final Odyssey.

Source: Prime Curios!

## Wednesday, November 19, 2014

### 1785

1785 = 3 x 5 x 7 x 17.

1785 is a multiple of 7 such that its digit sum is divisible by 7 (A216994).

1785 is a square pyramidal number (A000330). It is also a pentadecagonal number (A051867).

1785 is palindromic in base 5: 123321.

1785 is the sum of five positive fifth powers (A003350).

1785 divides 134 - 1.

Source: OEIS

## Tuesday, November 18, 2014

### 3900

3900 = 2 x 2 x 3 x 5 x 5 x 13.

3900 has a base 2 representation (111100111100) that is two copies of its base 5 representation (111100) concatenated (A175514). It is 330330 in base 4 (A045075) and 7474 in base 8 (A033079). It is 14241 in base 7 (palindromic).

3900 is the number of rooted trees with 15 nodes and 4 leaves (A055279).

3900 is the sum of four distinct powers of 5 (A038476).

3900 divides 496 - 1.

## Monday, November 17, 2014

### 3640

3640 = 2 x 2 x 2 x 5 x 7 x 13.

The sum of the digits of 3640 (13) is the largest prime factor of 3640 (A052021).

3640 is 111000111000111 in base 2 (binary) and 7070 in base 8. It is 11222211 in base 3, 320320 in base 4, and 4884 in base 9. It uses each of the digits 0, 1, 2, 3, 4 once in base 7 (13420).

3640 is a triple factorial number (A007661).

3640 is the number of regions in a regular 35-gon that are hexagons (A067153).

3640 divides 813 - 1.

Source: OEIS

## Friday, November 14, 2014

### 4699

4699 = 37 x 127.  4699 is a semiprime and each of its digits is a semiprime (A107342).

The sum of the digits of 4699 is 7 times the number of digits (A061424).

4699 is a nonagonal number (A001106).

4699 is 11133 in base 8 (A032915).

4699 is the number of 8-digit squares such that there is at least one permutation that is also a square (no initial zeros) (A177952).

4699 divides 2818 - 1.

Source: OEIS

## Thursday, November 13, 2014

### 1767

1767 = 3 x 19 x 31. The sum 3 + 19 + 31 = 53 is a prime number (A176877).

1767 is 123213 in base 4.

1767 is the sum of the digit reversals of the first 47 natural numbers (A062918).

1767 is a number n such that n, n + 1, and the sum of these two numbers each have three distinct prime factors (A168629).

1767 divides 942 - 1.

Source: OEIS

## Wednesday, November 12, 2014

### 8866

8866 = 2 x 11 x 13 x 31.

8866 is 2022202 in base 4. 8866 is 3334 in base 14 (A032838).

8866 is the number of necklaces with 6 black beads and 20 white beads (A032191).

8866 is the number of tilings of a 5 x 6 rectangle using pentominoes of any but the L shape (A247768).

8866 is a truncated triangular pyramid number (A051941).

8866 divides 876 - 1.

Source: OEIS

## Tuesday, November 11, 2014

### 6662

6662 = 2 x 3331.

The sum of the reciprocals of the digits of 6662 is 1 (A037268).

6662 is a beastly (or hateful) number because it contains the string 666 (A051003).

6662 is the number of 3-dimensional polyominoes (or polycubes) with 8 cells and trivial symmetry group (A066453).

6662 and the square of 6662 use only the digits 2, 3, 4, 6, and 8 (A137072).

6662 has the same set of digits in base 4 (1220012) and base 9 (10112) (A037427).

Source: OEIS

## Monday, November 10, 2014

### 5356

5356 = 2 x 2 x 13 x 103.

5356 is the 103rd triangular number. It is also a centered nonagonal number (A060544). It is a triangular number whose digit reversal is a semiprime (A115742). It is also a triangular number for which the sum of digits is a prime number (A117512).

5356 is the number of inequivalent ways to place a pair of checkers on a 17 x 17 board (A014409).

5356 is the number of complete squares that fit inside a circle with radius 42, drawn on squared paper (A119677).

5356 divides 4712 - 1.

5356 is 40444 in base 6 (A043388). It is 12354 in base 8.

Source: OEIS

## Friday, November 7, 2014

### 5377

5377 = 19 x 283.

5377 is the sum of four distinct powers of 4 (A038472).

5377 is a lucky number for which the product of the digits is also a lucky number (A118556).

5377 * 5379 = 28922883 (A116226).

5377 is a semiprime n such that 3 x n - 2 is a square (A112393): 3 x 5377 - 2 = 16129 = 1272.

5377 divides 456 - 1.

Source: OEIS

## Thursday, November 6, 2014

### 1669

1669 is a prime number.

1667 and 1669 form a twin prime pair.

1669 is the smallest prime that appears in the same position as its own value when the Roman numerals (from 1 to 3999) are placed in lexicographic order. The other primes with this property are 3623 and 3631.

1669 is the smallest number whose 9th power has 29 digits.

16692 = 2785561, and 278 * (5/5) * 6 + 1 = 1669.

1669 has a representation as the sum of two squares: 1669 = 152 + 382.

1669 is the hypotenuse of a primitive Pythagorean triple: 16692 = 11402 + 12192.

Source: Prime Curios!

## Wednesday, November 5, 2014

### 3600

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5.

3600 is a perfect square (A159991). It is both the sum and the difference of two primes (A106575).

3600 has a representation as a sum of two squares: 3600 = 362 + 482.

3600 is the order of a perfect group.

3600 is 11221100 in base 3 (A033001). It is 2100 in base 12 and 1100 in base 15.

3600 is a concentric hexadecagonal number (A195146).

3600 is the number of seconds in an hour.

Source: Number Gossip

## Tuesday, November 4, 2014

### 1160

1160 = 2 x 2 x 2 x 5 x 29.

1160 is divisible by the sum of its prime factors (40) (A046346).

1160 is an octagonal number (A000567).

1160 is a cake number (A000125). It is the maximum number of pieces into which a cylindrical cake can be cut with 19 straight-plane cuts.

The sum of the squares of the first 1160 primes is prime (A098561).

1160 is the smaller of two consecutive numbers each divisible by a cube (A068140).

1160 is 1120222 in base 3, 102020 in base 4, and 2210 in base 8. It is 3245 in base 7. It is 808 in base 12 and 404 in base 17. It is 488 in base 16.

Source: Number Gossip

## Monday, November 3, 2014

### 1130

1130 = 2 x 5 x 113. It is the product of three distinct Sophie Germain primes (A157346).

1130 is a Perrin number (A001608).

1130 is a number whose sum of digits is 5 (A052219). The sum of the digits of 1130 in base 2 (10001101010) is also 5 (A037308). It is a multiple of 5 with a digit sum of 5 (A069540).

Every base 6 digit of 1130 (5122) is a base 8 digit of 1130 (2152) (A037399).

1130 is the first of a pair of consecutive sphenic numbers (the product of three distinct primes) (A215217).

1130 has two representations as a sum of two squares: 1130 = 132 + 312 = 172 + 292.

1130 divides 698 - 1.

## Friday, October 31, 2014

### 8666

8666 = 2 x 7 x 619.

8666 has a 9th root whose decimal part starts with the digits 1 to 9 in some order.

8666 is a beastly number (A051003).

8666 is the number of permutations of length 21 that avoid the patterns 123 and 4312 (A116699).

8666 is a number n such that n, n + 1, n + 2, and n + 3 are not divisible by any of their nonzero digits (A244358).

8666 is a number n such that n ends with 6 and is the difference of cubes in at least one way (A038861).

## Thursday, October 30, 2014

### 2430

2430 = 2 x 3 x 3 x 3 x 3 x 3 x 5.

2430 is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 18.

2430 is 3300 in base 9.

2430 is the sum of two powers of 3 (A055235).

2430 is the product of all distinct numbers formed by permuting digits of 2430 (A061147).

2430 is a number divisible by the square of the sum of its digits (A072081).

2430 divides 9127 - 1.

## Wednesday, October 29, 2014

### 3564

3564 = 2 x 2 x 3 x 3 x 3 x 3 x 11.

3564 is 11220000 in base 3.

3564 is a concentric hendecagonal number (A195043).

3564 is both an abundant number and a Smith number (A098835).

3564 is a number n such that n together with its double and triple contain every digit (A120564).

3564 divides 8918 - 1.

3564 divides 11 + 22 + 33 + . . . + 35643564 (A135189).

## Tuesday, October 28, 2014

### 5675

5675 = 5 x 5 x 227.

5675 is the number of monic polynomials of degree 13 with integer coefficients whose complex roots are all in the unit disk (A051894).

5675 is 2777 in base 13.

5675 is an alternating sum of decreasing powers (A083326).

## Monday, October 27, 2014

### 3387

3387 = 3 x 1129.

3387 is the largest of three consecutive semiprimes (A115393).

3387 is the number of different keys with 7 cuts, depths between 1 and 7 and depth difference at most 1 between adjacent cut depths (A002714).

3387 and 33387 end with the same two digits (A067749).

3387 divides 318 - 1.

Source: OEIS

## Friday, October 24, 2014

### 5102

5102 = 2 x 2551.

5102 is a semiprime whose digit sum is a perfect cube (A245021).

5102 divides 516 - 1.

5102 is 6888 in base 9 (A043487).

Source: OEIS

## Thursday, October 23, 2014

### 1295

1295 = 5 x 7 x 37.

1295 is 5555 in base 6 (A097252).

1295 has the representation 64 - 1 (A123865 and A024062). It is a subperfect power (A045542).

1295 is the sum of consecutive cubes (A217843).

1295 is the difference of two positive fourth powers (A147857).

Every run of digits of 1295 in base 4 has length 2 (A033002): 110033.

## Wednesday, October 22, 2014

### 8123

8123 is a prime number.

8123 is a prime that can be written as a sum of 13 consecutive primes (A127341).

8123 is a prime p such that q - p = 24, where q is the next prime after p (A098974).

8123 represented in base 4 has 2 2s and 4 3s (A045147): 1332323.

8123 is a prime with an equal number of 0s, 1s, and 2s in its base three representation (A174976): 102010212.

8123 is a prime, as is 812318123281233812348123581236812378123881239 (A244271).

Source: OEIS

## Tuesday, October 21, 2014

### 1845

1845 = 3 x 3 x 5 x 41.

1845 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).

1845 is the number of ways to place three points on a triangular grid of side 7 so that no two of them are adjacent (A238569).

1845 is the sum of 11 nonzero 6th powers (A003367).

1845 has two representations as a sum of two squares: 1845 = 92 + 422 = 182 + 392.

1845 divides 734 - 1.

Source: OEIS

## Monday, October 20, 2014

### 1837

1837 = 11 x 167.

1837 is a centered dodecagonal number (or a star number) (A003154).

1837 is a concentric hexagonal number (A032528).

1837 is a value of n for which 2n (3674) and 7n (12859) together use each of the digits 1 to 9 exactly once.

1837, 1838, and 1839 are consecutive semiprimes (A056809).

1837 is the number of intersections of diagonals in the interior of a regular 18-gon (A006561).

## Friday, October 17, 2014

### 3203

3203 is a prime number.

Reversing the digits of 3203 also produces a prime (A109309).

3203 has the property that if each digit is replaced by its square, the resulting number is a square.

3203 is a prime whose digit sum is 8 (A062343).

3203 is the smallest prime whose decimal expansion begins with concatenation of the first two primes in descending order (A171154).

## Thursday, October 16, 2014

### 9199

9199 is a prime number (A020457).

9199 is a prime whose digit sum is the perfect number 28 (A048517).

9199 is a prime number with every digit a perfect square (A061246).

9199 and the square of 9199 have the same digit sum (A058370).

9199 is the sum of 15 consecutive primes (A161612).

9199 is 243244 in base 5.

9199 divides 4021 - 1.

9199 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Wednesday, October 15, 2014

### 6488

6488 = 2 x 2 x 2 x 811.

6488 would be prime if preceded and followed by 1, 3, 7, or 9 (A059677).

6488 is the maximum number of regions into which 47 triangles divide the plane (A077588).

6488 is a number n such that n! has a square number of digits (A006488).

6488 divides 1518 - 1.

6488 is 22220022 in base 3. It is 8808 in base 9 (A097255 and A043487).