%I
%S 0,0,0,1,0,1,2,0,2,0,0,1,0,3,2,0,0,1,0,3,4,3,0,0,0,0,2,3,0,1,0,3,2,0,
%T 0,5,0,3,0,0,0,1,6,0,4,0,6,5,0,3,0,3,6,5,0,0,2,0,0,1,0,3,2,0,6,0,6,0,
%U 0,3,0,1,6,0,2,0,6,5,0,3,0,0,0,5,0,9,4,3,0,7,0,3,2,0,6,0,0,3,0,9,0,1,6,0,2,0,0,1,0
%N a(n) = least k>0 such that nk^2 and n+k^2 are both primes.
%C If n is a square then a(n)=sqrt(n)1 or 0.
%C Also if n is a square and a(n)=sqrt(n)1 then sqrt(n) is a term in A178659.
%C First appearances of k for k=1..58 are at n = 4, 7, 14, 21, 36, 43, 90, 117, 86, 111, 210, 149, 768, 201, 236, 285, 468, 329, 366, 411, 446, 1137, 534, 647, 654, 807, 770, 885, 900, 911, 3090, 1665, 1192, 2415, 1296, 1313, 4212, 2163, 1600, 1671, 5448, 1769, 2040, 1941, 2054, 3207, 2214, 2333, 5340, 2601, 2792, 7725, 2814, 3095, 3054, 5913, 3442, 4377.
%C Among the first 10000 terms, the first missing values are 59, 79, 82, 83, 89, 91, 92, 94, 97, 98, 100.
%o (PARI) k=1;while(k^2<n,if(isprime(nk^2)&&isprime(n+k^2),return(k));k++);0
%o vector(50,n,a(n)) \\ _Derek Orr_, Feb 11 2015
%Y Cf. A068501, A082467, A178659.
%K nonn
%O 1,7
%A _Zak Seidov_, Feb 10 2015
