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.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

Cf. A016067, A046921.

Programs

Haskell

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

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 *)

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