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A254761
One half of the fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = A007519(n), n >= 1 (primes congruent to 1 mod 8).
7
1, 1, 1, 2, 3, 1, 2, 2, 4, 5, 2, 1, 4, 6, 1, 4, 2, 1, 7, 3, 1, 7, 8, 2, 4, 1, 5, 6, 5, 3, 2, 8, 10, 2, 6, 1, 7, 8, 9, 10, 4, 7, 3, 2, 9, 1, 12, 7, 3, 5
OFFSET
1,4
COMMENTS
For the corresponding term x1(n) see A254760(n).
See A254760 also for the Nagell reference.
The least positive y solutions (that is the ones of the first class) for the primes +1 and -1 (mod 8) together (including in the first class also prime 2) are given in A002335.
FORMULA
A254760(n)^2 - 2*(2*a(n))^2 = A007519(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.
EXAMPLE
See A254760.
n = 3: 9^2 - 2*(2*1)^2 = 81 - 8 = 73.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 12 2015
STATUS
approved