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A083338 Number of partitions of odd numbers into three primes and of even numbers into two primes. 4
0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 4, 2, 3, 2, 5, 3, 5, 3, 5, 3, 7, 2, 7, 3, 6, 2, 9, 4, 8, 4, 9, 2, 10, 3, 11, 4, 10, 3, 12, 4, 13, 5, 12, 4, 15, 3, 16, 5, 14, 3, 17, 4, 16, 6, 16, 3, 19, 5, 21, 6, 20, 2, 20, 5, 22, 6, 21, 5, 22, 5, 28, 7, 24, 4, 25, 5, 29, 8, 27, 5, 29, 4, 33, 9, 29, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

a(n) > 0 for all n iff Goldbach's conjectures hold.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1001

Antti Karttunen, Scheme-program for computing A083338 and A083339

Eric Weisstein's World of Mathematics, Goldbach Conjecture.

Index entries for sequences related to Goldbach conjecture

FORMULA

a(n) = if n is even then A045917(n/2) else A054860((n-1)/2).

For even n: a(n) = A061358(n); for odd n: a(n) = A068307(n). - Antti Karttunen, Sep 14 2017

MATHEMATICA

f[n_] := Length@ IntegerPartitions[n, If[ OddQ@ n, {3}, {2}], Prime@ Range@ PrimePi@ n]; Array[f, 92] (* Robert G. Wilson v, Nov 28 2012 *)

CROSSREFS

Cf. A000607, A061358, A068307, A071335, A083339.

Sequence in context: A189684 A308176 A106493 * A241900 A204018 A261915

Adjacent sequences:  A083335 A083336 A083337 * A083339 A083340 A083341

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Apr 24 2003

STATUS

approved

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Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)