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

1,1

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A001358, A061358, A100949.

Sequence in context: A031256 A032730 A275274 * A084418 A226133 A125971

Adjacent sequences: A131831 A131832 A131833 * A131835 A131836 A131837

Keyword

nonn

Author

Jonathan Vos Post, Oct 04 2007

Extensions

Data corrected by Giovanni Resta, Jun 19 2016

Status

approved