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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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%I A322385 #13 Dec 06 2018 20:06:24
%S A322385 2,7,19,43,53,107,131,163,227,263,311,383,443,521,577,613,719,751,881,
%T A322385 1021,1193,1301,1307,1423,1619,1667,1699,1993,2003,2161,2309,2311,
%U A322385 2437,2539,2693,2939,2969,3167,3209,3671,3767,3779,3833,4423,4481,4597,4871,5147
%N A322385 2 and prime numbers whose prime index is a product of at least two not necessarily distinct prime numbers already in the sequence.
%C A322385 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.
%H A322385 Alois P. Heinz, <a href="/A322385/b322385.txt">Table of n, a(n) for n = 1..1000</a>
%e A322385 We have 1993 = prime(301) = prime(7 * 43). Since 7 and 43 already belong to the sequence, so does 1993.
%t A322385 ppQ[n_]:=And[PrimeQ[n],!PrimeQ[PrimePi[n]],And@@ppQ/@First/@If[n==2,{},FactorInteger[PrimePi[n]]]];
%t A322385 Select[Range[1000],ppQ]
%Y A322385 Cf. A000002, A001462, A007097, A079000, A079254, A277098, A280996, A291636, A304360, A320628, A322386.
%K A322385 nonn
%O A322385 1,1
%A A322385 _Gus Wiseman_, Dec 05 2018