cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A254766 #10 Feb 14 2015 23:50:14
%S A254766 5,11,9,17,13,23,21,17,27,35,23,21,41,31,29,39,37,53,33,31,41,59,39,
%T A254766 49,37,35,43,63,53,37,49,77,59,47,75,83,65,53,73,51,45,61,71,59,79,69,
%U A254766 95,55,49,101
%N 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).
%C A254766 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 A254766 The positive fundamental solutions of the first classes are given in (A254764(n), A254765(n)).
%C A254766 For comments and the Nagell reference see A254764.
%F A254766 a(n)^2 - 2*(A254929(n))^2 = A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F A254766 a(n) = 3*A254764(n) - 4*A254765(n), n >= 1.
%e A254766 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 A254766 Cf. A007522, A139487, A254929, A254764, A254765, A254760, A254761, A254762, A254763,
%K A254766 nonn,easy
%O A254766 1,1
%A A254766 _Wolfdieter Lang_, Feb 11 2015