

A254937


Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2  2*y^2 = A007519(n), n>=1 (primes congruent to 1 mod 8).


5



7, 9, 11, 15, 19, 13, 17, 19, 27, 31, 21, 19, 29, 37, 21, 31, 25, 23, 43, 29, 25, 45, 49, 29, 35, 27, 39, 43, 41, 35, 33, 53, 61, 35, 47, 33, 51, 55, 59, 63, 43, 53, 41, 39, 61, 37, 73, 55, 43
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OFFSET

1,1


COMMENTS

The corresponding positive fundamental solution x2(n) of this second class solutions is given in A254936(n).
See the comments and the Nagell reference in A254934.


LINKS

Table of n, a(n) for n=1..49.


FORMULA

A254936(n)^2  2*a(n)^2 = A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
a(n) = (2*A254934(n)  3*A254935(n)), n >= 1.


EXAMPLE

n = 2: 11^2  2*9^2 = 121  162 = 41.
a(2) = (2*3  3*5) = 9.
See also A254936.


CROSSREFS

Cf. A007519, A254936, A254934, A254935, A255234, A255248, A254760.
Sequence in context: A139058 A242103 A328454 * A222947 A107226 A252663
Adjacent sequences: A254934 A254935 A254936 * A254938 A254939 A254940


KEYWORD

nonn,look,easy


AUTHOR

Wolfdieter Lang, Feb 18 2015


STATUS

approved



