A233513 Triangle read by antidiagonals of the conjectured least index k > 2 of Fibonacci-like sequence f(i+2) = f(i+1) + f(i), with f(1)=m 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, 4, 3, 3, 3, 4, 10, 9, 0, 0, 5, 4, 7, 11, 10, 8, 0, 0, 4, 0, 0, 6, 9, 12, 7, 0, 4, 3, 3, 3, 3, 3, 3, 3, 3, 11, 0, 0, 4, 5, 8, 6, 0, 11, 10, 0, 6, 0, 0, 4, 0, 5, 13, 0, 0, 0, 0, 11, 7, 0, 8, 4, 0, 0, 5, 4, 12, 5, 0, 8, 9, 0, 6, 0, 4, 11, 0, 0, 0, 4, 7, 0

Offset

1,1

Comments

Does this sequence have a maximum value? In row 340, the maximum value is 46.

References

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

Links

T. D. Noe, Rows n = 1..100 of triangle, flattened

Example

The rectangular array begins
12, 11, 3, 4, 0, 10, 0, 3, 11, 10,…  (A236506)
4, 3, 10, 5, 8, 6, 3, 0, 0, 0,...
3, 9, 4, 0, 9, 3, 0, 6, 0, 5,...
0, 7, 0, 12, 3, 4, 0, 11, 0, 7,...
11, 4, 7, 3, 5, 0, 7, 8, 0, 4,...
0, 0, 3, 8, 4, 0, 9, 5, 0, 3,...
4, 3, 6, 0, 8, 0, 0, 0, 3, 0,...
3, 0, 5, 4, 6, 0, 0, 3, 14, 0,...
11, 13, 0, 0, 13, 5, 3, 4, 12, 10,...
0, 0, 4, 0, 0, 3, 0, 0, 0, 0,...

Mathematica

squareQ[n_] := IntegerQ[Sqrt[n]]; nn = 100; t2 = Table[f = {m, n - m + 1}; 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, 15}, {m, n}]

Crossrefs

Cf. A236506 (m=1).

Sequence in context: A038336 A236506 A087868 * A175042 A255134 A109065

Adjacent sequences: A233510 A233511 A233512 * A233514 A233515 A233516

Keyword

nonn,tabl

Author

T. D. Noe, Jan 28 2014

Status

approved