A236506 Conjectured least index k > 2 of Fibonacci-like sequence f(i+2) = f(i+1) + f(i), with f(1)=1 and f(2)=n, such that f(k) is a square, or k=0 if squares do not exist in the corresponding sequence.

12, 11, 3, 4, 0, 10, 0, 3, 11, 10, 0, 4, 0, 0, 3, 0, 0, 11, 15, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3, 0, 0, 12, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 11, 10, 0, 4

Offset

1,1

Comments

n=1 corresponds to the usual Fibonacci sequence, for which f(12) = 144 = 12^2, so a(1)=12.

References

J. H. E. Cohn, On square Fibonacci numbers, J. London Math. Soc. 39 (1964), 537-540.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

a(6)=10 since f(10) = 361 = 19^2 for sequence starting f(1)=1, f(2)=6.

Mathematica

squareQ[n_] := IntegerQ[Sqrt[n]]; nn = 100; Table[f = {1, n}; Do[AppendTo[f, f[[-1]] + f[[-2]]], {i, 3, nn}]; k = 2; While[k++; k <= nn && ! squareQ[f[[k]]]]; If[k > nn, k = 0]; k, {n, 100}] (* T. D. Noe, Jan 28 2014 *)

Crossrefs

Cf. A000045 (Fibonacci numbers), A236534.

Cf. A233513 (triangular array for f(1)=m and f(2)=n).

Sequence in context: A297910 A298503 A038336 * A087868 A233513 A175042

Adjacent sequences: A236503 A236504 A236505 * A236507 A236508 A236509

Keyword

nonn

Author

Carmine Suriano, Jan 27 2014

Status

approved