A256503 Smallest k>=1 such that n^2 + (n+1)^2 + ... + (n+k)^2 is prime or a(n)=0 if there is no such k.

1, 1, 5, 1, 1, 2, 1, 0, 1, 0, 0, 1, 5, 1, 0, 0, 1, 5, 1, 0, 5, 1, 5, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 5, 1, 0, 0, 1, 0, 0, 0, 0, 1, 5, 0, 1, 5, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 5, 0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 5, 1, 0, 1, 1, 2, 1

Offset: 1

Author

Vladimir Shevelev, Mar 31 2015

Keywords

• nonn

Comments

Every term is either 0 or 1 or 2 or 5.

a(n)=0 if and only if n is in A256385.

Crossrefs

Cf. A000290, A256385, A089306.

Formula

1) if 2n^2+2n+1 is prime, then a(n)=1;

2) if 2n^2+2n+1 is not prime, but 3n^2+6n+5 is prime, then a(n)=2;

3) if 2n^2+2n+1 and 3n^2+6n+5 are both composite numbers, but 6n^2+30n+55 is prime, then a(n)=5;

4) otherwise, a(n)=0.

Extensions

More terms from Peter J. C. Moses, Mar 31 2015