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 A131834 #11 Jun 14 2024 12:37:17
%S A131834 6,9,11,17,38,51,62,88,93,98,122,148,152,188,222,232,248,266,272,296,
%T A131834 308,326,388,398,458,488,500,518,572,602,686,692,708,860,912,972,992,
%U A131834 1068,1112,1128,1146,1152,1270,1272,1340,1356,1422,1536,1542,1578
%N A131834 Indices of records in A100949.
%F A131834 Numbers n such that the number of partitions of n into a prime and a semiprime is a record.
%e A131834 a(15) = 222 because there are 22 partitions of n into a prime and a semiprime and that 22 is a record.
%e A131834 For n = 6, 9, 11, 17, 38, 51, 62, 88, 93, 98, 122, 148, 152, 188, 222, A100949(n) = 1, 2, 3, 5, 6, 8, 10, 11, 12, 13, 16, 17, 19, 21, 22.
%t A131834 nPar[n_] := Length@ Select[Prime@ Range[ PrimePi@ n], PrimeOmega[n - #] == 2 &]; r = 0; L = {}; n = 2; While[Length[L] < 50, p = nPar[++n]; If[p > r, r = p; AppendTo[L, n]]]; L (* _Giovanni Resta_, Jun 19 2016 *)
%t A131834 DeleteDuplicates[Table[{n,Count[Sort/@(PrimeOmega/@IntegerPartitions[n,{2}]),{1,2}]},{n,1600}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]]//Rest (* _Harvey P. Dale_, Jun 14 2024 *)
%Y A131834 Cf. A000040, A001358, A061358, A100949.
%K A131834 nonn
%O A131834 1,1
%A A131834 _Jonathan Vos Post_, Oct 04 2007
%E A131834 Data corrected by _Giovanni Resta_, Jun 19 2016