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 A178041 #18 Feb 16 2025 08:33:12
%S A178041 1,2,3,3,5,6,6,6,8,10,13,14,13,18,21,17,21,30,21,32,23,37,27,45,35,34,
%T A178041 54,43,60,61,67,44,52,55,79,58,89,57,92,100,111,69,119,76,83,122,91,
%U A178041 89,94,102,147,146,106,159,116,176,125,190,119,195,202,136,230,148,154,222
%N A178041 Number of ways to represent the n-th prime (which has a nonzero number of such representations) as the sum of 4 distinct primes.
%H A178041 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture</a>,
%e A178041 a(1) = 1 because 17 = 2+3+5+7 is the unique solution for the smallest such prime.
%e A178041 a(2) = 2 because 23 = 2+3+5+13 = 2+3+7+11 are the only two solutions for the 2nd smallest such prime.
%e A178041 a(3) = 3 because 29 = 2+3+5+19 = 2+3+7+17 = 2+3+11+13 are the only 3 solutions for the 3rd smallest such prime.
%e A178041 a(4) = 3 because 31 = 2+3+7+19 = 2+5+7+17 = 2+5+11+13 are the only 3 solutions for the 4th smallest such prime.
%e A178041 a(5) = 5 because 37 = 2+3+13+19 = 2+5+7+23 = 2+5+11+19 = 2+5+13+17 = 2+7+11+17 are the only 5 solutions for the 5th smallest such prime.
%t A178041 max=367;lim=PrimePi[max];p4=Sort[Total/@Subsets[Prime[Range[lim]],{4}]];p4p=Select[p4,PrimeQ[#]&&#<=max&]; s={};Do[c=Count[p4p,Prime[p]];If[c>0,AppendTo[s,c]],{p,lim}];s (* _James C. McMahon_, Jan 11 2025 *)
%Y A178041 Cf. A000040, A038609 (sum of 2 distinct primes), A124867 (sum of 3 distinct primes), A124868 (not the sum of 3 distinct primes), A124884 (not the sum of n distinct primes).
%K A178041 easy,nonn
%O A178041 1,2
%A A178041 _Jonathan Vos Post_, May 17 2010
%E A178041 Extended by _Zak Seidov_