Numbers beginning 23 consecutive numbers whose squares sum to a square.
7, 17, 881, 1351, 42787, 65337, 2053401, 3135331, 98520967
1
We do not have enough terms to determine the recursion formula. It is conjectured that this sequence satisfies an 11-th order linear recurrence.
T. D. Noe, Plot of 9 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 7^2 + 8^2 + … + 29^2 = 92^2.
(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[#, # + 23 - 1]]] &]
Cf. A001032, A001652, A106521, A094196, S000278-S000283, S000284.
nonn,more
T. D. Noe, Oct 08 2014