A131834 Indices of records in A100949.

6, 9, 11, 17, 38, 51, 62, 88, 93, 98, 122, 148, 152, 188, 222, 232, 248, 266, 272, 296, 308, 326, 388, 398, 458, 488, 500, 518, 572, 602, 686, 692, 708, 860, 912, 972, 992, 1068, 1112, 1128, 1146, 1152, 1270, 1272, 1340, 1356, 1422, 1536, 1542, 1578

Offset: 1

Author

Jonathan Vos Post, Oct 04 2007

Keywords

• nonn

Examples

			a(15) = 222 because there are 22 partitions of n into a prime and a semiprime and that 22 is a record.
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.
		

Crossrefs

Cf. A000040, A001358, A061358, A100949.

Programs

Mathematica

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 *)
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 *)

Formula

Numbers n such that the number of partitions of n into a prime and a semiprime is a record.

Extensions

Data corrected by Giovanni Resta, Jun 19 2016