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A255234
One half of the fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007522(n), n>=1 (primes congruent to 7 mod 8).
5
2, 3, 5, 4, 8, 5, 7, 11, 8, 7, 12, 14, 8, 11, 13, 10, 12, 10, 16, 18, 15, 11, 17, 14, 19, 21, 20, 14, 17, 26, 21, 14, 18, 23, 16, 15, 19, 24, 18, 26, 32, 23, 20, 25, 19, 22, 17, 29, 35, 18, 28, 25, 32, 21, 34, 19, 29, 23, 26, 31, 22, 33, 28, 37, 39, 41, 24
OFFSET
1,1
COMMENTS
The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A255233(n).
See the comments and the Nagell reference in A254938.
FORMULA
A255233(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
a(n) = -(A254938(n) - 3*A255232(n)), n >= 1.
EXAMPLE
n = 2: 7^2 - 2*(2*3)^2 = 49 - 72 = -23 = - A007522(2).
a(3) = -(1 - 3*2) = 5.
See also A255233.
CROSSREFS
KEYWORD
nonn,look,easy
AUTHOR
Wolfdieter Lang, Feb 19 2015
EXTENSIONS
More terms from Colin Barker, Feb 24 2015
STATUS
approved