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%I #15 Sep 19 2020 23:03:58
%S 1,2,4,6,9,11,13,17,18,20,22,26,28,33,37,39,41,49,50,52,54,56,57,66,
%T 73,76,81,85,86,97,100,102,106,109,114,121,129,134,137,145,148,153,
%U 161,162,164,166,172,177,181,182,191,193,196,198,201,211,220,225,226
%N a(1)=1 and, for n>1, a(n) is the smallest positive integer greater than a(n-1) such that a(n)+a(k) is not a square for k=1,2,...,n-1.
%C See A005652 for the case where the sum of two terms is never a Fibonacci number.
%H Matthew Conroy, <a href="/A203988/b203988.txt">Table of n, a(n) for n = 1..10000</a>
%t t = {1}; Do[k = t[[-1]] + 1; While[Length[Select[t, ! IntegerQ[Sqrt[# + k]] &]] < Length[t], k++]; AppendTo[t, k], {n, 2, 100}]; t (* _T. D. Noe_, Jan 10 2012 *)
%o (PARI) seq(n)={my(a=vector(n)); a[1]=1; for(n=2, n, my(m=a[n-1], f=1); while(f, m++; f=0; for(k=1, n-1, f=issquare(a[k]+m); if(f, break))); a[n]=m); a} \\ _Andrew Howroyd_, Sep 19 2020
%Y Cf. A005652.
%K nonn
%O 1,2
%A _John W. Layman_, Jan 09 2012
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