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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

%I

%S 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,

%T 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,

%U 0,0,5,4,12,5,0,8,9,0,6,0,4,11,0,0,0,4,7,0

%N 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.

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

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

%H T. D. Noe, <a href="/A233513/b233513.txt">Rows n = 1..100 of triangle, flattened</a>

%e The rectangular array begins

%e 12, 11, 3, 4, 0, 10, 0, 3, 11, 10,… (A236506)

%e 4, 3, 10, 5, 8, 6, 3, 0, 0, 0,...

%e 3, 9, 4, 0, 9, 3, 0, 6, 0, 5,...

%e 0, 7, 0, 12, 3, 4, 0, 11, 0, 7,...

%e 11, 4, 7, 3, 5, 0, 7, 8, 0, 4,...

%e 0, 0, 3, 8, 4, 0, 9, 5, 0, 3,...

%e 4, 3, 6, 0, 8, 0, 0, 0, 3, 0,...

%e 3, 0, 5, 4, 6, 0, 0, 3, 14, 0,...

%e 11, 13, 0, 0, 13, 5, 3, 4, 12, 10,...

%e 0, 0, 4, 0, 0, 3, 0, 0, 0, 0,...

%t 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}]

%Y Cf. A236506 (m=1).

%K nonn,tabl

%O 1,1

%A _T. D. Noe_, Jan 28 2014

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)