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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.
2
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
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 05 2018
STATUS
approved