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A007697
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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)
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7
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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)
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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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.
Index entries for sequences related to Goldbach conjecture
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a007697 n = 2 * (fromJust $ findIndex (>= n) a046921_list) + 1
-- Reinhard Zumkeller, Apr 03 2013
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CROSSREFS
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Cf. A016067, A046921.
Sequence in context: A018621 A236940 A024469 * A055202 A158016 A281998
Adjacent sequences: A007694 A007695 A007696 * A007698 A007699 A007700
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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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
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STATUS
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approved
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