

A264439


The y 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 even D(n) = A264354(n).


2



1, 17, 1, 49, 21287, 1, 23, 97, 1, 48727, 161, 151, 1, 21387679, 241, 1826021057, 1, 11692649642023, 7, 337, 3903396217, 1, 294125365483681, 17, 449, 7, 1994828801, 1, 6399911, 4798348971487087, 577, 119, 7867888313, 1, 437071, 161131189369, 721, 273849896195263, 20783, 262759
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OFFSET

1,2


COMMENTS

The corresponding x2(n) value is given by A264438(n). The positive fundamental solution (x1(n), y1(n)) of the first class is given by (2*A261247(n), A261248(n)).
There is only one class of proper solutions for those D = D(n) = A264354(n) values leading to (x1(n), y1(n)) = (x2(n), y2(n)).


LINKS

Table of n, a(n) for n=1..40.


EXAMPLE

n=1: D(1) = 8, (2*2)^2  8*1^2 = +8. The first class positive fundamental solution was identical, thus there is only one class of proper solutions for D = 8.
n=5: D(5) = 124, (2*118521)^2  124*21287^2 = +8. The first class solution was (2*39)^2  124*7^2 = +8. Thus there are two classes, conjugated to each other for this D value.


CROSSREFS

Cf. A264354, A261247 (x1/2), A261248 (y1), A264438 (x2/2), A263012 (odd D), A264349, A264350, A264351, A264353.
Sequence in context: A040305 A189120 A102292 * A279363 A295576 A223519
Adjacent sequences: A264436 A264437 A264438 * A264440 A264441 A264442


KEYWORD

nonn


AUTHOR

Wolfdieter Lang, Nov 19 2015


STATUS

approved



