S000280


Numbers beginning 47 consecutive numbers whose squares sum to a square.

539, 731, 53931, 72359, 5178999, 6947895

1

S000280

We do not have enough terms to determine the recursion formula.

T. D. Noe, Plot of 6 terms

Moshe Laub, Squares Expressible as a Sum of n Consecutive Squares, Advanced Problem 6552, Amer. Math. Monthly 97 (1990), 622-625.

The smallest example is 539^2 + 540^2 + … + 585^2 = 3854^2.

(Mma) g[m0_, m1_] := (1 - m0 + m1) (-m0 + 2 m0^2 + m1 + 2 m0 m1 + 2 m1^2)/6; Select[Range[100000], IntegerQ[Sqrt[g[#, # + 47 - 1]]] &]

Cf. A001032A001652A106521A094196, S000277-S000283S000284.

nonn,more

T. D. Noe, Oct 08 2014

© Tony D Noe 2014-2015