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A324695
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Lexicographically earliest sequence of positive integers whose prime indices are not already in the sequence.
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54
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1, 3, 7, 9, 11, 13, 19, 21, 27, 29, 33, 37, 39, 43, 47, 49, 53, 57, 59, 61, 63, 71, 77, 79, 81, 83, 87, 89, 91, 97, 99, 101, 107, 111, 113, 117, 121, 127, 129, 131, 133, 139, 141, 143, 147, 149, 151, 159, 163, 169, 171, 173, 177, 179, 181, 183, 189, 193, 197
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
3: {2}
7: {4}
9: {2,2}
11: {5}
13: {6}
19: {8}
21: {2,4}
27: {2,2,2}
29: {10}
33: {2,5}
37: {12}
39: {2,6}
43: {14}
47: {15}
49: {4,4}
53: {16}
57: {2,8}
59: {17}
61: {18}
63: {2,2,4}
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MATHEMATICA
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aQ[n_]:=And@@Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>!aQ[PrimePi[p]]];
Select[Range[100], aQ]
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CROSSREFS
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Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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