## 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