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

5, 13, 29, 53, 85, 173, 229, 293, 365, 445, 533, 629, 733, 965, 1093, 1229, 1373, 1685, 1853, 2029, 2213, 2405, 2605, 2813, 3029, 3253, 3485, 3973, 4229, 4493, 4765, 5045, 5333, 5629, 5933, 6245, 6565, 6893, 7229, 7573, 8285, 8653, 9029, 9413, 9805

Offset

1,1

Comments

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

References

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

Links

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

Maple

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

Mathematica

Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]
Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* Navvye Anand, Jun 20 2024 *)

Prog

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

Crossrefs

Cf. A078370, A087475 (supersequences).

Sequence in context: A130230 A106931 A078370 * A247903 A350687 A240130

Adjacent sequences: A308461 A308462 A308463 * A308465 A308466 A308467

Keyword

nonn,easy

Author

Alonso del Arte, May 29 2019

Status

approved