A254766 - OEIS

%I #10 Feb 14 2015 23:50:14

%S 5,11,9,17,13,23,21,17,27,35,23,21,41,31,29,39,37,53,33,31,41,59,39,

%T 49,37,35,43,63,53,37,49,77,59,47,75,83,65,53,73,51,45,61,71,59,79,69,

%U 95,55,49,101

%N 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).

%C 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).

%C The positive fundamental solutions of the first classes are given in (A254764(n), A254765(n)).

%C For comments and the Nagell reference see A254764.

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

%F a(n) = 3*A254764(n) - 4*A254765(n), n >= 1.

%e 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]], ...

%Y Cf. A007522, A139487, A254929, A254764, A254765, A254760, A254761, A254762, A254763,

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 11 2015