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A002374
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Largest prime <= n in any decomposition of 2n into a sum of two odd primes.
(Formerly M2278 N0900)
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10
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3, 3, 5, 5, 7, 5, 7, 7, 11, 11, 13, 11, 13, 13, 17, 17, 19, 17, 19, 13, 23, 19, 19, 23, 23, 19, 29, 29, 31, 23, 29, 31, 29, 31, 37, 29, 37, 37, 41, 41, 43, 41, 43, 31, 47, 43, 37, 47, 43, 43, 53, 47, 43, 53, 53, 43, 59, 59, 61, 53, 59, 61, 59, 61, 67, 53, 67, 67, 71, 71, 73, 59
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| The g.f. (3-3*z+2*z**2+z**3-z**4-2*z**5+2*z**6)/((z+1)*(z**2-z+1)*(z-1)**2) conjectured by S. Plouffe in his 1992 dissertation is wrong.
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REFERENCES
| D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 80.
N. Pipping, Neue Tafeln fuer das Goldbarsche Gesetz nebst Berichtungen zu den Haussnerschen Tafeln, Finska Vetenskaps-Societeten, Comment. Physico Math.. 4 (No. 4, 1927), 27 pp.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 3..10000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| a(n) = n - A047160(n) = A112823(n) (for n >= 3). [From Jason Kimberley, Aug 31 2011]
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MATHEMATICA
| nmax = 74; a[n_] := (k = 0; While[k < n && (!PrimeQ[n-k] || !PrimeQ[n+k]), k++]; If[k == n, n+1, n-k]); Table[a[n], {n, 3, nmax}](* From Jean-François Alcover, Nov 14 2011, after Jason Kimberley *)
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CROSSREFS
| Cf. A002372, A002373, A014092.
Essentially the same as A112823. [From Franklin T. Adams-Watters, Jan 25 2010]
Sequence in context: A035299 A021302 A004649 * A110560 A141424 A172170
Adjacent sequences: A002371 A002372 A002373 * A002375 A002376 A002377
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Sep 21 2000
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