Sunday, April 10, 2016

Number of the day: 6908

Properties of the number 6908:

6908 = 22 × 11 × 157 is the 6019th composite number and is not squarefree.
6908 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 3120 totatives.
6908 has a prime digit sum 23 in base 10.
6908 = 17282 - 17262 = 1682 - 1462 is the difference of 2 nonnegative squares in 2 ways.
6908 is the difference of 2 positive pentagonal numbers in 2 ways.
6908 is not the sum of 3 positive squares.
69082 is the sum of 2 positive squares in 1 way.
6908 is a divisor of 15836 - 1.
6908 in base 29 = 866 and consists of only the digits '6' and '8'.
6908 in base 33 = 6bb and consists of only the digits '6' and 'b'.
6908 in base 41 = 44K and consists of only the digits '4' and 'K'.

The number 6908 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A096813: Backwards row convergent of triangle A096811, in which A096811(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and (k-2).
A113650: Fibonacci(p-J(p,5)) mod p^2, where p is the n-th prime and J is the Jacobi symbol.
A185943: Riordan array ((1/(1-x))^m,x*A000108(x)), m=2.
A206464: Number of length-n Catalan-RGS (restricted growth strings) such that the RGS is a valid mixed radix number in falling factorial basis.
A217354: Numbers n such that 8^n + 3 is prime.
A224038: T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing
A234991: T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A257827: Positive integers whose square is the sum of 96 consecutive squares.
A260841: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101

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