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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 11 23:26 EDT 2020. Contains 335652 sequences. (Running on oeis4.)