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 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. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified September 27 18:40 EDT 2020. Contains 337386 sequences. (Running on oeis4.)