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 A355250 #11 Jan 31 2025 14:04:41
%S A355250 2,2,3,3,3,3,5,5,5,5,7,7,5,7,7,7,7,7,11,11,11,11,13,13,11,13,13,13,13,
%T A355250 13,17,17,17,17,19,19,17,19,19,19,13,19,23,23,19,23,19,23,23,23,23,23,
%U A355250 19,23,29,29,29,29,31,31,23,31,29,31,31,31,29,31,31,31,37,37,29,37
%N A355250 Largest prime appearing among the "middle parts" of the partitions of n into (exactly) 3 prime parts.
%H A355250 Harvey P. Dale, <a href="/A355250/b355250.txt">Table of n, a(n) for n = 6..1000</a>
%H A355250 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%e A355250 a(17) = 7; of the 4 ways to write 17 as the sum of 3 primes, 7 is the largest "middle" part: 2+2+13 = 3+3+11 = 3+7+7 = 5+5+7.
%t A355250 Table[Max[Select[IntegerPartitions[n,{3}],AllTrue[#,PrimeQ]&][[;;,2]]],{n,6,90}] (* _Harvey P. Dale_, Jan 31 2025 *)
%Y A355250 Cf. A164024.
%K A355250 nonn
%O A355250 6,1
%A A355250 _Wesley Ivan Hurt_, Jun 25 2022