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A254929
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).
4
3, 7, 5, 11, 7, 15, 13, 9, 17, 23, 13, 11, 27, 19, 17, 25, 23, 35, 19, 17, 25, 39, 23, 31, 21, 19, 25, 41, 33, 19, 29, 51, 37, 27, 49, 55, 41, 31, 47, 29, 23, 37, 45, 35, 51, 43, 63, 31, 25, 67
OFFSET
1,1
COMMENTS
The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A254766(n).
See the comments and the Nagell reference in A254764.
FORMULA
A254766(n)^2 - 2*a(n)^2 = A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
a(n) = 2*A254764(n) - 3*A254765(n), n >= 1.
EXAMPLE
n = 2: 11^2 - 2*7^2 = 121 - 98 = 23.
The smallest positive solution is (x1(2), y1(2)) = (5, 1) from (A254764(2), A254765(2)).
See also A254766.
a(4) = 2*7 - 3*1 = 11.
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 11 2015
STATUS
approved