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Search: id:A045917
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| A045917 |
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From Goldbach problem: number of decompositions of 2n into unordered sums of two primes. |
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28
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| 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, 4, 3, 4, 5, 4, 3, 5, 3, 4, 6, 3, 5, 6, 2, 5, 6, 5, 5, 7, 4, 5, 8, 5, 4, 9, 4, 5, 7, 3, 6, 8, 5, 6, 8, 6, 7, 10, 6, 6, 12, 4, 5, 10, 3, 7, 9, 6, 5, 8, 7, 8, 11, 6, 5, 12, 4, 8, 11, 5, 8, 10, 5, 6, 13, 9, 6, 11, 7, 7, 14, 6, 8, 13, 5, 8, 11, 7, 9
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Note that A002375 (which differs only at the n=2 term) is the main entry for this sequence.
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REFERENCES
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Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, MA, 1996, Chapter 12, Pages 236-257.
H. Halberstam and H. E. Richert, 1974, "Sieve methods", Academic press, London, New York, San Francisco.
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LINKS
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H. J. Smith, Table of n, a(n) for n = 1..20000
M. Herkommer, Goldbach Conjecture Research
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
G. Xiao, WIMS server, Goldbach
Index entries for sequences related to Goldbach conjecture
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FORMULA
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From Halberstam and Richert : a(n)<(8+0(1))*c(n)*n/ln(n)^2 where c(n)=prod(p>2,(1-1/(p-1)^2))*prod(p|n,p>2,(p-1)/(p-2)). It is conjectured that the factor 8 can be replaced by 2. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 16 2002
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MATHEMATICA
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f[n_] := Length[Select[2n - Prime[Range[PrimePi[n]]], PrimeQ]]; Table[ f[n], {n, 100}] (Paul Abbott, Jan 11 2005)
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CROSSREFS
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A002375 (which differs only at the n=2 term) is the main entry for this sequence.
A023036 is the first appearance of n and A000954 is the last (assumed) appearance of n.
Sequence in context: A053597 A094570 A002375 this_sequence A029379 A058776 A029228
Adjacent sequences: A045914 A045915 A045916 this_sequence A045918 A045919 A045920
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KEYWORD
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nice,nonn,easy
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AUTHOR
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Felice Russo (felice.russo(AT)katamail.com)
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