A007697 Smallest odd number expressible in at least n ways as p+2*m^2 where p is 1 or a prime and m >= 0. (Formerly M2292)

1, 3, 13, 19, 55, 61, 139, 139, 181, 181, 391, 439, 559, 619, 619, 829, 859, 1069, 1081, 1459, 1489, 1609, 1741, 1951, 2029, 2341, 2341, 3331, 3331, 3331, 3961, 4189, 4189, 4261, 4801, 4801, 5911, 5911, 5911, 6319, 6319, 6319, 8251, 8251, 8251, 8251, 8251

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.

L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.

M. Stern, Sur une assertion de Goldbach relative aux nombres impairs, Nouvelles Annales Math., 15 (1856) pp. 23-24.

Index entries for sequences related to Goldbach conjecture

Mathematica

max = 9000; sp = Outer[Plus, Prepend[Prime /@ Range[PrimePi[max]], 1], 2*Range[0, Ceiling[Sqrt[max/2]]]^2] // Flatten // Sort // Split;
a[1] = 3; a[n_] := (sel = Select[sp, Length[#] >= n &];
If[sel == {}, {}, sel[[1, 1]]]); a /@ Range[47]
(* Jean-François Alcover, Apr 29 2011 *)

Prog

(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a007697 n = 2 * (fromJust $ findIndex (>= n) a046921_list) + 1
-- Reinhard Zumkeller, Apr 03 2013

Crossrefs

Cf. A016067, A046921.

Sequence in context: A018621 A236940 A024469 * A055202 A158016 A281998

Adjacent sequences: A007694 A007695 A007696 * A007698 A007699 A007700

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

Stern and Hardy-Littlewood references suggested by Ctibor O. Zizka, Apr 14 2008

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar

a(1) changed to 1 at the suggestion of Donovan Johnson by N. J. A. Sloane, May 10 2011

Status

approved