%I #17 May 13 2013 01:54:22
%S 1,2,3,5,13,17,23,37,49,53,67,83,97,101,103,113,137,149,151,163,167,
%T 173,263,317,337,347,353,383,401,433,451,487,503,551,563,601,701,751,
%U 773,947,967,977,983,1013,1033,1049,1051,1087,1187,1201,1249,1283,1333
%N a(n+1) is the smallest integer m > a(n) such that all of sums (a(i))^2 + m^2, i=1..n are squarefree.
%C All terms except for a(2)=2 are odd.
%H Charles R Greathouse IV, <a href="/A214802/b214802.txt">Table of n, a(n) for n = 1..1000</a>
%t s={1}; m=1; Do[f=0; Do[If[!SquareFreeQ[s[[i]]^2+p^2], f=1; Break[]], {i,m}]; If[f<1, AppendTo[s, p]; m++], {p, 2, 10^3}]; s
%o (PARI) v=List([1]); for(m=2,1e3,for(j=1,#v,if(issquare(m^2+v[j]^2), next(2))); listput(v,m)); Vec(v) \\ _Charles R Greathouse IV_, Jul 30 2012
%Y Cf. A203988, A214735.
%K nonn
%O 1,2
%A _Zak Seidov_, Jul 28 2012
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