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A061358
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Number of ways of writing n = p+q with p, q primes and p >= q.
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40
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0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 3, 0, 3, 1, 3, 0, 2, 0, 3, 1, 2, 1, 4, 0, 4, 0, 2, 1, 3, 0, 4, 1, 3, 1, 4, 0, 5, 1, 4, 0, 3, 0, 5, 1, 3, 0, 4, 0, 6, 1, 3, 1, 5, 0, 6, 0, 2, 1, 5, 0, 6, 1, 5, 1, 5, 0, 7, 0, 4, 1, 5, 0, 8, 1, 5, 0, 4, 0, 9, 1, 4, 0, 5, 0, 7, 0, 3, 1, 6, 0, 8, 1, 5, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| (1) For an odd number n, a(n) = 0 if n-2 is not a prime else a(n) = 1. (2) a(2n) is at least 1, according to Goldbach's conjecture.
a(A014092(n)) = 0; a(A014091(n)) > 0; a(A067187(n)) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 22 2004
Number of partitions of n into two primes.
Number of unordered ways of writing n as the sum of two primes.
a(2*n) = A068307(2*n+2). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 08 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10000
Index entries for sequences related to Goldbach conjecture
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FORMULA
| G.f.=sum(sum(x^(p(i)+p(j)), i=1..j), j=1..infinity), where p(k) is the k-th prime. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
A065577(n)=a(10^n). Cf. A073610, A107318.
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EXAMPLE
| a[22] = 3 because 22 can be written as 3+19, 5+17 and 11+11.
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MAPLE
| g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j), j=1..30): gser:=series(g, x=0, 110): seq(coeff(gser, x, n), n=0..105); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
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MATHEMATICA
| a[n_] := Length[Select[n - Prime[Range[PrimePi[n/2]]], PrimeQ]]; Table[a[n], {n, 0, 100}] (Paul Abbott, Jan 11 2005)
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CROSSREFS
| a(2n) is A045917.
Cf. A067187, A067188, A067189, A067190, A067191.
Cf. A063610
Sequence in context: A055639 A156542 A066360 * A025866 A048881 A026931
Adjacent sequences: A061355 A061356 A061357 * A061359 A061360 A061361
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KEYWORD
| nonn,easy
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AUTHOR
| Amarnath_murthy (amarnath_murthy(AT)yahoo.com), Apr 28 2001
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), May 15 2001
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