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A155216
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Number of decompositions of positive even numbers 2n into unordered sums of a prime and a prime or semiprime (Chen's partitions)
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1
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0, 1, 2, 2, 2, 3, 3, 4, 3, 4, 5, 5, 6, 7, 4, 6, 6, 7, 8, 8, 7, 8, 9, 8, 8, 10, 9, 10, 10, 10, 13, 11, 10, 12, 11, 12, 12, 14, 12, 13, 14, 13, 13, 15, 13, 15, 15, 17, 16, 15, 15, 15, 16, 18, 16, 16, 18, 17, 19, 17, 20, 19, 19, 18, 18, 20, 19, 20, 21, 20, 18, 22, 21, 22, 20, 23, 19, 22
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| According to Chen's result, the terms of this sequence are positive, at least for sufficiently large n.
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REFERENCES
| J. R. Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes, Kexue Tongbao,17(1966),385-386.
J. R. Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica, 16(1973),157-176
P. M. Ross, On Chen's theorem that each large even number has the form (p1+p2) or (p1+p2p3), J. London Math. Soc. (2) 10(1975), 500-506.
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LINKS
| V. Shevelev, Binary additive problems: recursions for numbers of representations
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MAPLE
| A155216 := proc(n) local a, p, q, twon ; twon := 2*n ; a := 0 ; for i from 1 do p := ithprime(i) ; if ithprime(i) > twon then break; end if; q := twon -ithprime(i) ; if isprime(q) and q>= p then a := a+1 ; end if; end do: for i from 1 do p := ithprime(i) ; if ithprime(i) > twon then break; end if; q := twon -ithprime(i) ; if isA001358(q) then a := a+1 ; end if; end do: return a; end proc: seq(A155216(n), n=1..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2010]
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CROSSREFS
| Sequence in context: A107325 A003050 A070868 * A064144 A077105 A173752
Adjacent sequences: A155213 A155214 A155215 * A155217 A155218 A155219
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KEYWORD
| nonn
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AUTHOR
| Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jan 22 2009
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EXTENSIONS
| Terms beyond a(21) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 26 2010
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