A108714 a(n)=minimal value of k, such that n^2+k^2 or (n^2+k^2)/2 are primes.

1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 7, 2, 1, 1, 1, 2, 5, 1, 1, 4, 5, 3, 1, 1, 1, 2, 5, 1, 11, 4, 3, 2, 5, 1, 1, 2, 3, 1, 1, 4, 5, 3, 9, 1, 5, 2, 13, 1, 7, 1, 3, 3

Offset: 1

Author

Robin Garcia, Jun 20 2005

Keywords

• nonn

Comments

I am attempting to complete a proof that for every natural number n, there is at least one prime of the form n^2+k^2 or (n^2+k^2)/2 with 1<=k<=n.

Examples

			a(3)=1 because (3^2+1)/2=5 (prime)
a(7)=2 ------> 7^2+2^2=53 (prime)
a(12)=7 -----> 12^2+7^2=193 (prime)
a(23)=3 -----> (23^2+3^2)/2=269 (prime)
a(48)=13 ----> 48^2+13^2=2473 (prime)