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A083338 Number of partitions of odd numbers into three primes and of even numbers into two primes. 4

%I

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A083338/b083338.txt">Table of n, a(n) for n = 1..1001</a>

%H Antti Karttunen, <a href="/A083338/a083338.txt">Scheme-program for computing A083338 and A083339</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture.</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

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

%F For even n: a(n) = A061358(n); for odd n: a(n) = A068307(n). - _Antti Karttunen_, Sep 14 2017

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

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

%K nonn,look

%O 1,9

%A _Reinhard Zumkeller_, Apr 24 2003

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Last modified August 22 12:33 EDT 2019. Contains 326177 sequences. (Running on oeis4.)