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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)
7
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
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.
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
Sequence in context: A018621 A236940 A024469 * A055202 A158016 A281998
KEYWORD
nonn,nice,easy
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