## S000648

The order of the difference equation that solves the equation x^2 + (x + S000647(n))^2 = y^2.

3, 7, 11, 19, 15, 31, 19, 55, 43, 51, 23, 91, 55, 163, 71, 27, 127, 67, 151, 271, 91, 31, 163, 99, 79, 211, 487, 379, 111, 35, 199, 251, 451, 127, 91, 271, 811, 487, 131, 295, 39, 235, 351, 631, 155, 103, 331, 1459, 1135, 163, 595, 751, 151, 379, 43, 271, 451, 1351, 811, 183, 115, 391, 491

1

All orders have the form 4k-1 for k = 1, 2, 3,…. See S000649.

T. D. Noe, Plot of 63 terms

(Mma) (* the numbers used for d come from S000647 *) Join[{3}, Table[td = {}; n = -2 d; c = {}; done = False; While[! done, If[PerfectSquareQ[n^2 + (n + d)^2], AppendTo[td, n]; If[Length[td] > 5 && EvenQ[Length[td]/2], len = Length[td]; s = td[[1]] - td[[2]] - 6*td[[len/2]] + 6*td[[len/2 + 1]] + td[[len - 1]]; done = (s == td[[len]])]]; n++]; len - 1, {d, {7, 49, 119, 343, 833, 2401, 2737, 5831, 14161, 16807, 19159, 40817, 84847, 99127}}]]

Cf. S000647, S000649.

nonn,hard

T. D. Noe, Jun 04 2015

© Tony D Noe 2014-2015