A322385 2 and prime numbers whose prime index is a product of at least two not necessarily distinct prime numbers already in the sequence.

2, 7, 19, 43, 53, 107, 131, 163, 227, 263, 311, 383, 443, 521, 577, 613, 719, 751, 881, 1021, 1193, 1301, 1307, 1423, 1619, 1667, 1699, 1993, 2003, 2161, 2309, 2311, 2437, 2539, 2693, 2939, 2969, 3167, 3209, 3671, 3767, 3779, 3833, 4423, 4481, 4597, 4871, 5147

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

We have 1993 = prime(301) = prime(7 * 43). Since 7 and 43 already belong to the sequence, so does 1993.

Mathematica

ppQ[n_]:=And[PrimeQ[n], !PrimeQ[PrimePi[n]], And@@ppQ/@First/@If[n==2, {}, FactorInteger[PrimePi[n]]]];
Select[Range[1000], ppQ]

Crossrefs

Cf. A000002, A001462, A007097, A079000, A079254, A277098, A280996, A291636, A304360, A320628, A322386.

Sequence in context: A152461 A215208 A100119 * A350170 A220697 A078842

Adjacent sequences: A322382 A322383 A322384 * A322386 A322387 A322388

Keyword

nonn

Author

Gus Wiseman, Dec 05 2018

Status

approved