cp's OEIS Frontend

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.

A308464 Squarefree numbers of the form m^2 + 4.

This page as a plain text file.
%I A308464 #24 Dec 09 2024 16:38:00
%S A308464 5,13,29,53,85,173,229,293,365,445,533,629,733,965,1093,1229,1373,
%T A308464 1685,1853,2029,2213,2405,2605,2813,3029,3253,3485,3973,4229,4493,
%U A308464 4765,5045,5333,5629,5933,6245,6565,6893,7229,7573,8285,8653,9029,9413,9805
%N A308464 Squarefree numbers of the form m^2 + 4.
%C A308464 Yokoi's conjecture posits that, except for most of the values less than 365, the ring of algebraic integers of Q(sqrt(a(n))) has class number greater than 1. Only one counterexample to this conjecture may exist, and it would also be a counterexample to the generalized Riemann hypothesis, according to Mollin (1996).
%C A308464 All terms == 5 (mod 8). - _Robert Israel_, Jun 05 2019
%D A308464 Richard A. Mollin, Quadratics. Boca Raton, Florida: CRC Press (1996): 176 - 177.
%H A308464 Robert Israel, <a href="/A308464/b308464.txt">Table of n, a(n) for n = 1..10000</a>
%p A308464 select(numtheory:-issqrfree,[seq(m^2+4,m=1..1000,2)]); # _Robert Israel_, Jun 05 2019
%t A308464 Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]
%t A308464 Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* _Navvye Anand_, Jun 20 2024 *)
%o A308464 (PARI) is(n) = issquarefree(n) && issquare(n-4) \\ _Felix Fröhlich_, May 29 2019
%Y A308464 Cf. A078370, A087475 (supersequences).
%K A308464 nonn,easy
%O A308464 1,1
%A A308464 _Alonso del Arte_, May 29 2019