A264351 - OEIS

A264351

The x member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for odd D(n) = A263012(n).

29, 1223, 1040241, 9217, 3642669, 445435, 122279, 3667, 441089445, 1034361, 700801, 866477098293, 536018000953, 13456978719, 74857, 111814836531, 2150319955, 991403378623407, 20008281106509024285, 7993723517, 17651941238270751, 12685, 5754260987908903, 3427370031, 401477253306854423, 87725171, 225660404935077273, 539908248773809, 7742211688546213, 91867215744119283021, 16849, 2767937250852453, 14617581481552992324155240733, 5404928819007703, 1310525

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OFFSET

1,1

COMMENTS

The corresponding y = y2(n) member are given by A264350(n).

See A263012 for details and examples.

LINKS

Table of n, a(n) for n=1..35.

FORMULA

a(n)^2 - D(n)*y2(n)^2 = 8 with D(n) = A263012(n) and y2(n) = A264351(n), n >= 1.

EXAMPLE

n=1: 29^2 - 17*7^2 = 8. n=4: 9217^2 - 89*977^2 = 8.