## S000482

Square root of the numbers in S000481.

6, 9, 14, 14, 14, 19, 22, 30, 35, 49, 58, 78, 90, 126, 234, 405, 611, 1598, 4182, 10947, 28658, 75026, 196419, 514230, 1346270, 3524579, 9227466, 24157818, 63245987, 165580142, 433494438, 1134903171, 2971215074, 7778742050, 20365011075, 53316291174, 139583862446

1

Starting with the 17th number, 611, the numbers appear to satisfy a linear recurrence, which will be explored in subsequent sequences.

T. D. Noe, Plot of 60 terms

T. D. Noe, Table of 60 terms

Eric W. Weisstein, MathWorld: Fibonacci Number

(Mma) nn = 55; PerfectSquareQ[n_] := JacobiSymbol[n, 13] =!= -1 && JacobiSymbol[n, 19] =!= -1 && JacobiSymbol[n, 17] =!= -1 && JacobiSymbol[n, 23] =!= -1 && IntegerQ[Sqrt[n]]; f2 = Table[Fibonacci[n]^2, {n, 2, nn}]; t = {}; Do[If[a >= b >= c >= d && (a != b || a != c || a != d || b != c || b != d || c != d), n = a + b + c + d; If[PerfectSquareQ[n], AppendTo[t, n]]], {a, f2}, {b, f2}, {c, f2}, {d, f2}]; Sqrt[t]

Cf. S000481-S000490.

nonn

T. D. Noe, Feb 18 2015

© Tony D Noe 2014-2015