

A324697


Lexicographically earliest sequence of positive integers > 1 that are prime or whose prime indices already belong to the sequence.


18



2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 41, 43, 45, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 75, 79, 81, 83, 85, 89, 93, 97, 99, 101, 103, 107, 109, 113, 115, 121, 123, 125, 127, 131, 135, 137, 139, 141, 149, 151, 153, 155, 157, 163, 165
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OFFSET

1,1


COMMENTS

A selfdescribing sequence, similar to A304360.
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

The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
15: {2,3}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
33: {2,5}
37: {12}
41: {13}
43: {14}
45: {2,2,3}


MATHEMATICA

aQ[n_]:=Switch[n, 1, False, _?PrimeQ, True, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]];
Select[Range[100], aQ]


CROSSREFS

Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.


KEYWORD

nonn


AUTHOR



STATUS

approved



