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 A255232 #26 May 28 2025 16:54:55
%S A255232 1,2,2,3,3,4,4,4,5,6,5,5,7,6,6,7,7,9,7,7,8,10,8,9,8,8,9,11,10,9,10,13,
%T A255232 11,10,13,14,12,11,13,11,11,12,13,12,14,13,16,12,12,17,13,14,13,16,13,
%U A255232 18,14,16,15,14,17,14,15,14,14,14,17,16,19,16,17,16,20,21,17,16,17,16,16
%N A255232 One half of the fundamental positive solution y = y1(n) of the first class of the Pell equation x^2 - 2*y^2 = -A007522(n), n >= 1 (primes congruent to 7 mod 8).
%C A255232 For the corresponding term x1(n) see A254938(n).
%C A255232 See A254938 also for the Nagell reference.
%C A255232 The least positive y solutions (that is those of the first class) for the primes +1 and -1 (mod 8) together (including prime 2) are given in A255246.
%H A255232 M. F. Hasler, <a href="/A255232/b255232.txt">Table of n, a(n) for n = 1..1000</a>, May 22 2025
%F A255232 A254938(n)^2 - 2*(2*a(n))^2 = -A007522(n) gives the smallest positive (proper) solution of this (generalized) Pell equation.
%e A255232 See A254938.
%e A255232 n = 3: 1^2 - 2*(2*2)^2 = 1 - 32 = -31 = -A007522(3).
%o A255232 (PARI) apply( {A255232(n, p=A007522(n))=Set(abs(qfbsolve(Qfb(-1, 0, 2), p, 1)))[1][2]\2}, [1..88]) \\ The 2nd optional arg allows to directly specify the prime. - _M. F. Hasler_, May 22 2025
%Y A255232 Cf. A007522 (primes == 7 mod 8), A254938 (corresponding x1 values), A255233 (x2 values), A255234 (y2 values), A255246, A254935.
%K A255232 nonn,easy
%O A255232 1,2
%A A255232 _Wolfdieter Lang_, Feb 18 2015
%E A255232 More terms from _Colin Barker_, Feb 23 2015
%E A255232 Double-checked and extended by _M. F. Hasler_, May 22 2025