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

Author

Reinhard Zumkeller, Apr 24 2003

Keywords

• nonn
• look

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

Crossrefs

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

Programs

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 *)

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