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%I #20 Sep 17 2017 22:38:57
%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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