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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
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
Sequence in context: A139058 A242103 A328454 * A222947 A107226 A252663
KEYWORD
nonn,look,easy
AUTHOR
Wolfdieter Lang, Feb 18 2015
STATUS
approved

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Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)