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 A254937 #16 May 23 2025 01:17:10
%S A254937 7,9,11,15,19,13,17,19,27,31,21,19,29,37,21,31,25,23,43,29,25,45,49,
%T A254937 29,35,27,39,43,41,35,33,53,61,35,47,33,51,55,59,63,43,53,41,39,61,37,
%U A254937 73,55,43,49,39,67,71,51,43,49,69,47,77,63,51,67,49,71,79,65,87,49,47,55,67,61,85,53
%N A254937 Fundamental positive solution y = y2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007519(n), n>=1 (primes congruent to 1 mod 8).
%C A254937 The corresponding positive fundamental solution x2(n) of this second class solutions is given in A254936(n).
%C A254937 See the comments and the Nagell reference in A254934.
%H A254937 M. F. Hasler, <a href="/A254937/b254937.txt">Table of n, a(n) for n = 1..1000</a>, May 22 2025
%F A254937 A254936(n)^2 - 2*a(n)^2 = -A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F A254937 a(n) = -(2*A254934(n) - 3*A254935(n)), n >= 1.
%e A254937 n = 2: 11^2 - 2*9^2 = 121 - 162 = -41.
%e A254937 a(2) = -(2*3 - 3*5) = 9.
%e A254937 See also A254936.
%o A254937 (PARI) apply( {A254937(n, p=A007519(n))=n=Set(abs(qfbsolve(Qfb(-1, 0, 2), p, 1)))[1]*[-2, 3]~}, [1..77]) \\ The 2nd optional arg allows to directly specify the prime. - _M. F. Hasler_, May 22 2025
%Y A254937 Cf. A007519 (primes == 1 mod 8), A254936 (x2-values), A254934 (first (class) solution x1), A254935 (y1), A255234 (y2/2 for primes == 7 mod 8), A255248, A254760.
%K A254937 nonn,easy
%O A254937 1,1
%A A254937 _Wolfdieter Lang_, Feb 18 2015
%E A254937 More terms from _M. F. Hasler_, May 22 2025