A322386 -id:A322386 - cp's OEIS frontend

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

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Gus Wiseman, Dec 05 2018

nonn

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.

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

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

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

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

cp's OEIS Frontend

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

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