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 A133204 #19 Jun 27 2025 10:54:40
%S A133204 5,13,29,37,41,53,61,101,109,113,137,149,157,173,181,197,229,269,277,
%T A133204 293,313,317,349,373,389,397,409,421,457,461,509,521,541,557,569,613,
%U A133204 653,661,677,701,709,733,757,761,773,797,809,821,829,853,857,877,941
%N A133204 Primes p such that the non-Pellian equation x^2-2py^2=-1 is solvable.
%C A133204 The sequence contains no primes congruent to 3 modulo 4 and all primes congruent to 5 modulo 8.
%C A133204 Different from A385224, primes p such that multiplicative order of -4 modulo p is odd: 593 is in A385224 (ord(-4,593) = 37), but it is not here (x^2 - 1186*y^2 = -1 has no solution); 1601 is not in A385224 (ord(-4,1601) = 200), but it is here (x^2 - 3202*y^2 = -1 has solution (1641,29)). - _Jianing Song_, Jun 22 2025
%H A133204 Vincenzo Librandi, <a href="/A133204/b133204.txt">Table of n, a(n) for n = 1..1000</a>
%H A133204 H. von Lienen, <a href="http://dx.doi.org/10.1016/0022-314X(78)90003-3">The quadratic form x^2-2py^2</a>, J. Number Theory 10 (1978), 10-15.
%t A133204 fQ[n_] := Solve[x^2 + 1 == 2 n*y^2, {x, y}, Integers] != {}; Select[ Prime@ Range@ 160, fQ] (* _Robert G. Wilson v_, Dec 19 2013 *)
%Y A133204 Subsequence of A002144 (primes congruent to 1 modulo 4).
%Y A133204 Contains A007521 (primes congruent to 5 or modulo 8) as a proper subsequence.
%Y A133204 Cf. A385224.
%K A133204 nonn
%O A133204 1,1
%A A133204 _David Brink_, Dec 29 2007