cp's OEIS Frontend

A324702 Lexicographically earliest sequence containing 2 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.

%I A324702 #8 Mar 11 2019 20:48:47
%S A324702 2,5,13,25,43,65,101,125,169,193,215,317,325,505,557,559,625,701,845,
%T A324702 965,1013,1075,1181,1313,1321,1585,1625,1849,2111,2161,2197,2509,2525,
%U A324702 2785,2795,3125,3505,3617,4049,4057,4121,4225,4343,4639,4825,5065,5297,5375
%N A324702 Lexicographically earliest sequence containing 2 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.
%C A324702 A self-describing sequence, similar to A304360.
%C A324702 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.
%C A324702 Also 2 and numbers whose prime indices belong to A324703.
%F A324702 a(n) = A324703(n) - 1.
%e A324702 The sequence of terms together with their prime indices begins:
%e A324702     2: {1}
%e A324702     5: {3}
%e A324702    13: {6}
%e A324702    25: {3,3}
%e A324702    43: {14}
%e A324702    65: {3,6}
%e A324702   101: {26}
%e A324702   125: {3,3,3}
%e A324702   169: {6,6}
%e A324702   193: {44}
%e A324702   215: {3,14}
%e A324702   317: {66}
%e A324702   325: {3,3,6}
%e A324702   505: {3,26}
%e A324702   557: {102}
%e A324702   559: {6,14}
%e A324702   625: {3,3,3,3}
%e A324702   701: {126}
%e A324702   845: {3,6,6}
%e A324702   965: {3,44}
%t A324702 aQ[n_]:=Switch[n,0,False,1,False,2,True,_,And@@Cases[FactorInteger[n],{p_,k_}:>aQ[PrimePi[p]-1]]];
%t A324702 Select[Range[100],aQ]
%Y A324702 Prime indices > 1 are A324703.
%Y A324702 Cf. A000002, A000720, A001222, A001462, A007097, A045965, A055396, A061395, A064989, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
%Y A324702 Cf. A324694, A324695, A324696, A324697, A324698, A324699, A324700, A324701, A324704, A324705.
%K A324702 nonn
%O A324702 1,1
%A A324702 _Gus Wiseman_, Mar 11 2019