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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
OFFSET
1,1
COMMENTS
A self-describing 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.
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 10 2019
STATUS
approved