

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
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OFFSET

1,2


REFERENCES

Godfrey Harold Hardy and John Edensor Littlewood, Some problems of `partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., 44 (1922), 170.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Moritz A. Stern, Sur un assertion de Goldbach relative aux nombres impairs, Nouvelles Annales Math. 15 (1856), 2324.


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000
L. Hodges, A lesserknown Goldbach conjecture, Math. Mag., 66 (1993), 4547.
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]
(* JeanFrançois 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 A178712
Adjacent sequences: A007694 A007695 A007696 * A007698 A007699 A007700


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Stern and HardyLittlewood 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.  N. J. A. Sloane, May 10 2011


STATUS

approved



