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%I #13 Mar 25 2015 01:59:03
%S 1,0,2,4,0,1,3,0,9,2,0,8,1,0,7,3,0,6,2,0,5,1,0,4,8,0,3,7,0,2,6,0,1,5,
%T 0,15,4,0,14,3,0,13,2,0,12,1,0,11,5,0,10,4,0,9,3,0,8,2,0,7,1,0,6,12,0,
%U 5,11,0,4,10,0,3,9,0,2,8,0,1,7,0,21,6,0,20,5,0,19,4,0,18,3,0,17,2
%N a(n) is the smallest positive number m such that n+3*m is a square, or 0 if no such m exists.
%F a(n)=0 iff n==2 mod 3 because 2 is quadratic nonresidue of 3.
%e 1 + 3*1 = 4 = 2^2, 3 + 3*2 = 9 = 3^2, 4 + 3*4 = 16 = 4^2.
%t Table[m = 1; If[Mod[n, 3] == 2, m = 0, While[! IntegerQ[Sqrt[n + 3*m]], m++]]; m, {n, 100}] (* _Michael De Vlieger_, Mar 20 2015 *)
%o (PARI) a(n)=if(n==Mod(2,3),return(0));m=1;while(!issquare(n+3*m),m++);m
%o vector(100,n,a(n)) \\ _Derek Orr_, Mar 22 2015
%Y Cf. A256243.
%K nonn,easy
%O 1,3
%A _Zak Seidov_, Mar 20 2015
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