This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A083338 #21 Feb 16 2025 08:32:49
%S A083338 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 A083338 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 A083338 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 A083338 Number of partitions of odd numbers into three primes and of even numbers into two primes.
%C A083338 a(n) > 0 for all n iff Goldbach's conjectures hold.
%H A083338 Antti Karttunen, <a href="/A083338/b083338.txt">Table of n, a(n) for n = 1..1001</a>
%H A083338 Antti Karttunen, <a href="/A083338/a083338.txt">Scheme-program for computing A083338 and A083339</a>
%H A083338 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture.</a>
%H A083338 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F A083338 a(n) = if n is even then A045917(n/2) else A054860((n-1)/2).
%F A083338 For even n: a(n) = A061358(n); for odd n: a(n) = A068307(n). - _Antti Karttunen_, Sep 14 2017
%t A083338 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 A083338 Cf. A000607, A061358, A068307, A071335, A083339.
%K A083338 nonn,look
%O A083338 1,9
%A A083338 _Reinhard Zumkeller_, Apr 24 2003