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 A229219 #16 Aug 22 2025 05:55:11
%S A229219 1,1,2,2,1,2,4,3,4,4,4,4,6,5,6,6,6,6,6,6,6,7,8,8,8,8,8,8,8,8,9,10,10,
%T A229219 9,10,10,10,10,10,10,10,10,10,10,12,11,12,12,12,12,12,12,12,12,12,12,
%U A229219 12,12,12,14,13,14,14,14,14,14,14,14,14,14,14,14,14,14
%N A229219 a(n) = maximal length of partitions of prime(n) into distinct primes.
%H A229219 David A. Corneth, <a href="/A229219/b229219.txt">Table of n, a(n) for n = 1..10000</a>
%H A229219 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/12048.html">Prime Curios! 11</a>
%H A229219 Wikipedia, <a href="http://en.wikipedia.org/wiki/Knapsack_problem">Knapsack problem</a>
%e A229219 a(11) = 4 because prime(11) = 31 = 2 + 3 + 7 + 19, but 31 is not a sum of 5 or more distinct primes.
%t A229219 nn = 20; p = Prime[Range[nn]]; s = Subsets[p]; t2 = Table[Select[s, Total[#] == n &], {n, p}]; Table[Max[Length /@ t2[[n]]], {n, nn}] (* _T. D. Noe_, Nov 13 2013 *)
%Y A229219 Cf. A000040, A070215.
%K A229219 nonn,changed
%O A229219 1,3
%A A229219 _Arkadiusz Wesolowski_, Nov 10 2013