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A324702
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Lexicographically earliest sequence containing 2 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.
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12
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2, 5, 13, 25, 43, 65, 101, 125, 169, 193, 215, 317, 325, 505, 557, 559, 625, 701, 845, 965, 1013, 1075, 1181, 1313, 1321, 1585, 1625, 1849, 2111, 2161, 2197, 2509, 2525, 2785, 2795, 3125, 3505, 3617, 4049, 4057, 4121, 4225, 4343, 4639, 4825, 5065, 5297, 5375
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OFFSET
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1,1
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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.
Also 2 and numbers whose prime indices belong to A324703.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
5: {3}
13: {6}
25: {3,3}
43: {14}
65: {3,6}
101: {26}
125: {3,3,3}
169: {6,6}
193: {44}
215: {3,14}
317: {66}
325: {3,3,6}
505: {3,26}
557: {102}
559: {6,14}
625: {3,3,3,3}
701: {126}
845: {3,6,6}
965: {3,44}
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MATHEMATICA
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aQ[n_]:=Switch[n, 0, False, 1, False, 2, True, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]-1]]];
Select[Range[100], aQ]
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CROSSREFS
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Cf. A000002, A000720, A001222, A001462, A007097, A045965, A055396, A061395, A064989, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
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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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