A083338 Number of partitions of odd numbers into three primes and of even numbers into two primes.

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

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: A354257 A106493 A309981 * A241900 A204018 A261915

Adjacent sequences: A083335 A083336 A083337 * A083339 A083340 A083341

Keyword

nonn,look

Author

Reinhard Zumkeller, Apr 24 2003

Status

approved