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 A255234 #21 May 28 2025 00:28:07
%S A255234 2,3,5,4,8,5,7,11,8,7,12,14,8,11,13,10,12,10,16,18,15,11,17,14,19,21,
%T A255234 20,14,17,26,21,14,18,23,16,15,19,24,18,26,32,23,20,25,19,22,17,29,35,
%U A255234 18,28,25,32,21,34,19,29,23,26,31,22,33,28,37,39,41,24,27,22,31,28,33,23,22,30
%N A255234 One half of the fundamental positive solution y = y2(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 A255234 The corresponding fundamental solution x2(n) of this second class of positive solutions is given in A255233(n).
%C A255234 See the comments and the Nagell reference in A254938.
%H A255234 M. F. Hasler, <a href="/A255234/b255234.txt">Table of n, a(n) for n = 1..1000</a>, May 22 2025
%F A255234 A255233(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F A255234 a(n) = -(A254938(n) - 3*A255232(n)), n >= 1.
%e A255234 n = 2: 7^2 - 2*(2*3)^2 = 49 - 72 = -23 = - A007522(2).
%e A255234 a(3) = -(1 - 3*2) = 5.
%e A255234 See also A255233.
%o A255234 (PARI) apply( {A255234(n, p=A007522(n))=Set(abs(qfbsolve(Qfb(-1, 0, 2), p, 1)))[1]*[-1,3/2]~}, [1..88]) \\ The 2nd optional arg allows to directly specify the prime. - _M. F. Hasler_, May 22 2025
%Y A255234 Cf. A007522, A255233, A254938, A255232, A254937.
%K A255234 nonn,look,easy
%O A255234 1,1
%A A255234 _Wolfdieter Lang_, Feb 19 2015
%E A255234 More terms from _Colin Barker_, Feb 24 2015
%E A255234 Double-checked and extended by _M. F. Hasler_, May 22 2025