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 A218007 #17 Jan 11 2023 11:33:55
%S A218007 1,2,3,3,4,4,5,4,5,4,5,4,6,5,7,5,7,5,8,6,9,6,9,7,10,7,10,5,10,6,12,7,
%T A218007 13,7,12,8,14,7,14,6,15,8,17,9,17,8,18,10,19,10,19,7,20,9,21,9,20,7,
%U A218007 21,11,25,11,24,9,26,11,27,9,24,8,28,12,30,13,29
%N A218007 Number of partitions of n into at most three primes (including 1).
%C A218007 The above sequence relies on the strong Goldbach's conjecture that any positive integer is the sum of at most three distinct terms from {1 union primes}.
%H A218007 T. D. Noe, <a href="/A218007/b218007.txt">Table of n, a(n) for n = 1..1000</a>
%e A218007 a(21)=9 as 21 = 1+1+19 = 2+19 = 1+3+17 = 2+2+17 = 1+7+13 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7
%t A218007 primeQ[p0_] := If[p0==1, True, PrimeQ[p0]]; SetAttributes[primeQ, Listable]; goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1; While[n<=Length[parts], If[Intersection[Flatten[primeQ[parts[[n]]]]][[1]] == True, count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]
%t A218007 Table[Length[Select[#/.(1->2)&/@IntegerPartitions[n,3],AllTrue[#,PrimeQ]&]],{n,80}] (* _Harvey P. Dale_, Jan 11 2023 *)
%Y A218007 Cf. A002375, A025583, A068307, A071335, A185101.
%K A218007 nonn
%O A218007 1,2
%A A218007 _Frank M Jackson_, Mar 26 2013