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.
%I A254931 #15 Oct 28 2019 07:44:14
%S A254931 3,4,7,5,8,11,7,12,15,10,8,13,16,9,14,17,23,13,18,11,27,14,19,12,22,
%T A254931 17,25,28,23,18,14,32,35,19,17,22,30,25,36,39,16,28,23,31,21,19,40,20,
%U A254931 18,38
%N A254931 Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = A001132(n), n >= 1, (primes congruent to 1 or 7 mod 8).
%C A254931 The corresponding terms x = x2(n) are given in A254930(n).
%C A254931 The y2-sequence for the second class for the primes congruent to 1 (mod 8), which are given in A007519, is 2*A254763. For the primes congruent to 7 (mod 8), given in A007522, the y2-sequence is A254929.
%C A254931 For comments and the Nagell reference see A254760.
%F A254931 A254930(n)^2 - 2*a(n)^2 = A001132(n), and a(n) is the second largest (proper) positive integer satisfying this (generalized) Pell equation.
%F A254931 a(n) = 2*A002334(n+1) - 3*A002335(n+1), n >= 1.
%e A254931 a(4) = 2*7 - 3*3 = 5.
%e A254931 A254930(4)^2 - 2*a(4)^2 = 9^2 - 2*5^2 = 31 = A001132(4) = A007522(3).
%e A254931 See A254930 for the first pairs (x2(n), y2(n)).
%t A254931 Reap[For[p = 2, p < 1000, p = NextPrime[p], If[MatchQ[Mod[p, 8], 1|7], rp = Reduce[x > 0 && y > 0 && x^2 - 2 y^2 == p, {x, y}, Integers]; If[rp =!= False, xy = {x, y} /. {ToRules[rp /. C[1] -> 1]}; y2 = xy[[-1, 2]] // Simplify; Print[y2]; Sow[y2]]]]][[2, 1]] (* _Jean-François Alcover_, Oct 28 2019 *)
%Y A254931 Cf. A254930, A001132, A002334, A002335, A007519, 2*A254763, A007522, A254929, A254760.
%K A254931 nonn,easy
%O A254931 1,1
%A A254931 _Wolfdieter Lang_, Feb 12 2015