1,1

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).

All terms == 5 (mod 8). - Robert Israel, Jun 05 2019

Richard A. Mollin, Quadratics. Boca Raton, Florida: CRC Press (1996): 176 - 177.

Robert Israel, Table of n, a(n) for n = 1..10000

select(numtheory:-issqrfree, [seq(m^2+4, m=1..1000, 2)]); # Robert Israel, Jun 05 2019

Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]

Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* Navvye Anand, Jun 20 2024 *)

(PARI) is(n) = issquarefree(n) && issquare(n-4) \\ Felix Fröhlich, May 29 2019

Cf. A078370, A087475 (supersequences).

Sequence in context: A130230 A106931 A078370 * A247903 A350687 A240130

Adjacent sequences: A308461 A308462 A308463 * A308465 A308466 A308467

nonn,easy

Alonso del Arte, May 29 2019

approved