A203988 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.

1, 2, 4, 6, 9, 11, 13, 17, 18, 20, 22, 26, 28, 33, 37, 39, 41, 49, 50, 52, 54, 56, 57, 66, 73, 76, 81, 85, 86, 97, 100, 102, 106, 109, 114, 121, 129, 134, 137, 145, 148, 153, 161, 162, 164, 166, 172, 177, 181, 182, 191, 193, 196, 198, 201, 211, 220, 225, 226

Offset: 1

Author

John W. Layman, Jan 09 2012

Keywords

• nonn

Comments

See A005652 for the case where the sum of two terms is never a Fibonacci number.

Links

• Matthew Conroy, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005652.

Programs

Mathematica

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 *)

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