A264349 The x member of the positive proper fundamental solution (x = x1(n), y = y1(n)) of the first class for the Pell equation x^2 - D(n)*y^2 = +8 for odd D(n) = A263012(n).

5, 7, 9, 217, 69, 11, 199, 13, 56445, 15, 6121, 46557, 17, 9567711, 127, 73829571, 19, 101080863, 21, 35927573, 1582431, 379, 23, 729, 167, 32899, 689581594497, 25, 1348157, 207495429, 1255, 27, 146613, 278601383, 29, 21751, 4777049027, 33814353, 19022653, 5062449, 31, 43541, 225

Offset

1,1

Comments

The corresponding y = y1(n) member is given by A264350(n).

See A263012 for details and examples.

Links

Table of n, a(n) for n=1..43.

Formula

a(n)^2 - D(n)*y1(n)^2 = 8 with D(n) = A263012(n) and y1(n) = A264350(n), n >= 1.

Example

n=1:  5^2 - 17*1^2  = 8. n=4: 217^2 - 89*23^2  = 8.

Crossrefs

Cf. A263011, A263012, A264350, A264351, A264353.

Sequence in context: A050888 A366312 A323004 * A320114 A364284 A059485

Adjacent sequences: A264346 A264347 A264348 * A264350 A264351 A264352

Keyword

nonn

Author

Wolfdieter Lang, Nov 17 2015

Status

approved