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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
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.
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.
KEYWORD
nonn,look,easy
AUTHOR
Wolfdieter Lang, Feb 18 2015
STATUS
approved