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 A299732 #44 Sep 25 2023 15:05:42
%S A299732 2,5,8,13,20,29,42,57,78,109,148,197,264,347,454,595,770,989,1272,
%T A299732 1619,2054,2601,3268,4087,5108,6347,7860,9713,11948,14653,17944,21881,
%U A299732 26614,32311,39102,47211,56910,68397,82038,98237,117354,139923,166580,197877,234672
%N A299732 a(n) has exactly (a(n) - n) / 2 partitions with exactly (a(n) - n) / 2 prime parts.
%C A299732 If B={b(n)} is the complement of A299731 then no number exists that has exactly b(n) partitions that have exactly b(n) prime parts, so this sequence lists only those numbers that can have the equality property.
%C A299732 Up to a(44) = 234672 (currently, the last term), except for 2,5,8, and 29, every term is the sum of distinct previous terms. Will this be true for all new terms?
%H A299732 J. Stauduhar, <a href="/A299732/a299732.py.txt">Python program.</a>
%F A299732 a(n) = 2*A299731(n) + n = 2*A222656(3*n,n) + n.
%e A299732 For n = 3: A299731(3) = 5. a(3) = 2*5 + 3 = 13. The five partitions of 13 that have exactly five prime parts are: (5,2,2,2,2), (3,3,3,2,2), (3,3,2,2,2,1), (3,2,2,2,2,1,1), and (2,2,2,2,2,1,1,1), so a(3) = 13.
%o A299732 (Python) # See Stauduhar link.
%Y A299732 Cf. A222656, A299730, A299731.
%K A299732 nonn
%O A299732 0,1
%A A299732 _J. Stauduhar_, Feb 18 2018