Numbers beginning 59 consecutive numbers whose squares sum to a square.
22, 38, 1100, 1438, 55498, 72120, 1196778, 1555042, 58858540, 76477844
1
We do not have enough terms to determine the recursion formula.
T. D. Noe, Plot of 10 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 22^2 + 23^2 + … + 80^2 = 413^2.
(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[#, # + 59 - 1]]] &]
Cf. A001032, A001652, A106521, A094196, S000277-S000283, S000284.
nonn,more
T. D. Noe, Oct 08 2014