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 A292082 #23 May 30 2025 23:14:19 %S A292082 3,17,577,665857 %N A292082 Primes p such that (p^2 - 1) / 2 is a square (A000290). %C A292082 Corresponding values of squares: 4, 144, 166464, 221682772224. %C A292082 Subsequence of A257553. %C A292082 Conjecture: sequence is finite. %C A292082 Numbers k such that (k^2 - 1) / 2 is a square are given by A001541, of which the only prime terms are 3, 17, 577, and 665857 (see _Alexander Adamchuk_'s Nov 24 2006 Comments entry there), so a(4) = 665857 is the last term of this sequence. - _Jon E. Schoenfield_, Nov 20 2017 %e A292082 Number 3 is in the sequence because (3^2 - 1) / 2 = 4 (square). %t A292082 Select[Prime[Range[55000]],IntegerQ[Sqrt[(#^2-1)/2]]&] (* _Harvey P. Dale_, Mar 10 2019 *) %o A292082 (Magma) [n: n in [3..1000000] | IsPrime(n) and IsSquare((n^2-1) / 2)]; %Y A292082 Cf. A088165 (primes p such that (p^2 + 1) / 2 is a square). %Y A292082 Cf. A000290, A002315, A257553. %K A292082 nonn,fini,full %O A292082 1,1 %A A292082 _Jaroslav Krizek_, Sep 12 2017