

A254766


Fundamental positive solution x = x2(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



5, 11, 9, 17, 13, 23, 21, 17, 27, 35, 23, 21, 41, 31, 29, 39, 37, 53, 33, 31, 41, 59, 39, 49, 37, 35, 43, 63, 53, 37, 49, 77, 59, 47, 75, 83, 65, 53, 73, 51, 45, 61, 71, 59, 79, 69, 95, 55, 49, 101
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OFFSET

1,1


COMMENTS

The corresponding term y = y2(n) of this fundamental solution of the second class of the (generalized) Pell equation x^2  2*y^2 = A007522(n) = 7 + 8*A139487(n) is given in A254929(n).
The positive fundamental solutions of the first classes are given in (A254764(n), A254765(n)).
For comments and the Nagell reference see A254764.


LINKS



FORMULA

a(n)^2  2*(A254929(n))^2 = A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.


EXAMPLE

The first pairs [x2(n), y2(n)] of the fundamental positive solutions of the second class are (we list the prime A007522(n) as first entry): [7,[5,3]], [23,[11,7]], [31,[9,5]], [47,[17,11]], [71,[13,7]], [79,[23,15]], [103,[21,13]], [127,[17,9]], [151,[27,17]], [167,[35,23]], [191,[23,13]], [199,[21,11]], [223,[41,27]], [239,[31,19]], [263,[29,17]], [271,[39,25]], ...


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



