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A324702
Lexicographically earliest sequence containing 2 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.
12
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
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.
Also 2 and numbers whose prime indices belong to A324703.
FORMULA
a(n) = A324703(n) - 1.
EXAMPLE
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}
MATHEMATICA
aQ[n_]:=Switch[n, 0, False, 1, False, 2, True, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]-1]]];
Select[Range[100], aQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 11 2019
STATUS
approved