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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 (list; graph; refs; listen; history; text; internal format)
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), 1-70.

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), 23-24.

LINKS

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

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

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-Fran├žois 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 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. - N. J. A. Sloane, May 10 2011

STATUS

approved

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Last modified October 24 14:26 EDT 2014. Contains 248516 sequences.