A263978 - OEIS

%I #6 Nov 07 2015 17:03:52

%S 2,3,2,5,2,5,2,3,0,3,0,7,2,11,2,5,2,5,0,3,0,5,0,5,0,5,2,5,0,11,0,3,2,

%T 5,2,5,2,3,0,3,0,5,0,19,2,5,2,13,0,7,0,3,0,11,0,11,2,3,0,13,0,3,0,11,

%U 2,29,2,5,0,3,0,5,2,5,0,5,0,7,0,7,0,3,0,11,2,11,2,3,0,11,0,7,0,5,2,5,2,3,0,3

%N Least prime p such that n^2 + p^2 is prime, or 0 if none.

%C When n is odd, n^2 + p^2 is composite for all odd primes p, so a(n) = 2 or 0 according as n^2 + 2^2 is prime or not.

%C The locations of the zeros are in A263722.

%C The location of the first occurrence of prime(n) is A263466(n).

%e a(1) = 2 since 1^2 + 2^2 = 5 is prime.

%e a(2) = 3 since 2^2 + 2^2 = 8 is not prime but 2^2 + 3^2 = 13 is prime.

%e a(9) = 0 since 9^2 + 2^2 = 85 is not prime.

%t f[n_] := If[OddQ[n] && ! PrimeQ[n^2 + 4], 0,

%t   Block[{p = 2}, While[! PrimeQ[n^2 + p^2] && p < 1500, p = NextPrime@p];

%t    p]]; Array[f, 100]

%Y Cf. A240130, A240131, A263466, A263721, A263722, A263726, A263977.

%K nonn

%O 1,1

%A _Jonathan Sondow_ and _Robert G. Wilson v_, Nov 06 2015