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A046927
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Number of ways to express 2n+1 as p+2q; p, q primes.
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7
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0, 0, 0, 1, 2, 2, 2, 2, 4, 2, 3, 3, 3, 4, 4, 2, 5, 3, 4, 4, 5, 4, 6, 4, 4, 7, 5, 3, 7, 3, 3, 7, 7, 5, 7, 4, 4, 8, 7, 5, 8, 4, 7, 8, 7, 4, 11, 5, 6, 9, 6, 5, 12, 6, 6, 10, 8, 6, 11, 7, 5, 11, 8, 6, 10, 6, 6, 13, 8, 5, 13, 6, 9, 12, 8, 6, 14, 8, 6, 11, 10, 9, 16, 5, 8, 13, 9, 9, 14, 7, 6, 14
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| This is related to a conjecture of Lemoine (also sometimes called Levy's conjecture, although Levy was anticipated by Lemoine 69 years earlier). - Zhi-Wei Sun, Jun 10 2008
The conjecture states that any odd number greater than 5 can be written as p+2q where p and q are primes.
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REFERENCES
| L. E. Dickson, "History of the Theory of Numbers", Vol. I (Amer. Math. Soc., Chelsea Publ., 1999); see p. 424.
E. Lemoine, L'intermediaire des math., 1(1894), 179; 3(1896), 151.
H. Levy, "On Goldbach's Conjecture", Math. Gaz. 47 (1963), 274.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10000
L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.
V. Shevelev, Binary additive problems: recursions for numbers of representations [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jan 22 2009]
Eric Weisstein's World of Mathematics, Levy's Conjecture
Index entries for sequences related to Goldbach conjecture
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CROSSREFS
| Cf. A194831 (records), A194830 (positions of records).
Sequence in context: A061389 A138011 A036555 * A084718 A154851 A037445
Adjacent sequences: A046924 A046925 A046926 * A046928 A046929 A046930
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Additional comments and references from Zhi-Wei Sun (zwsun(AT)nju.edu.cn), Jun 10 2008
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