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A324700 Lexicographically earliest sequence containing 0 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.

%I A324700 #8 Mar 11 2019 20:48:35
%S A324700 0,2,4,5,8,10,11,13,16,20,22,23,25,26,31,32,37,40,43,44,46,50,52,55,
%T A324700 59,62,64,65,73,74,80,83,86,88,89,92,100,101,103,104,110,115,118,121,
%U A324700 124,125,128,130,131,137,143,146,148,155,160,163,166,169,172,176
%N A324700 Lexicographically earliest sequence containing 0 and all positive integers > 1 whose prime indices minus 1 already belong to the sequence.
%C A324700 A self-describing sequence, similar to A304360.
%C A324700 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.
%F A324700 a(n) = A324701(n) - 1.
%e A324700 The sequence of terms together with their prime indices begins:
%e A324700    0
%e A324700    2: {1}
%e A324700    4: {1,1}
%e A324700    5: {3}
%e A324700    8: {1,1,1}
%e A324700   10: {1,3}
%e A324700   11: {5}
%e A324700   13: {6}
%e A324700   16: {1,1,1,1}
%e A324700   20: {1,1,3}
%e A324700   22: {1,5}
%e A324700   23: {9}
%e A324700   25: {3,3}
%e A324700   26: {1,6}
%e A324700   31: {11}
%e A324700   32: {1,1,1,1,1}
%e A324700   37: {12}
%e A324700   40: {1,1,1,3}
%e A324700   43: {14}
%e A324700   44: {1,1,5}
%t A324700 aQ[n_]:=Switch[n,0,True,1,False,_,And@@Cases[FactorInteger[n],{p_,k_}:>aQ[PrimePi[p]-1]]];
%t A324700 Select[Range[0,100],aQ]
%Y A324700 Prime indices are A324701.
%Y A324700 Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
%Y A324700 Cf. A324694, A324695, A324696, A324697, A324698, A324699, A324702, A324703, A324704, A324705.
%K A324700 nonn
%O A324700 1,2
%A A324700 _Gus Wiseman_, Mar 10 2019