A324700 - OEIS

%I #8 Mar 11 2019 20:48:35

%S 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 59,62,64,65,73,74,80,83,86,88,89,92,100,101,103,104,110,115,118,121,

%U 124,125,128,130,131,137,143,146,148,155,160,163,166,169,172,176

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

%C A self-describing sequence, similar to A304360.

%C 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 a(n) = A324701(n) - 1.

%e The sequence of terms together with their prime indices begins:

%e    0

%e    2: {1}

%e    4: {1,1}

%e    5: {3}

%e    8: {1,1,1}

%e   10: {1,3}

%e   11: {5}

%e   13: {6}

%e   16: {1,1,1,1}

%e   20: {1,1,3}

%e   22: {1,5}

%e   23: {9}

%e   25: {3,3}

%e   26: {1,6}

%e   31: {11}

%e   32: {1,1,1,1,1}

%e   37: {12}

%e   40: {1,1,1,3}

%e   43: {14}

%e   44: {1,1,5}

%t aQ[n_]:=Switch[n,0,True,1,False,_,And@@Cases[FactorInteger[n],{p_,k_}:>aQ[PrimePi[p]-1]]];

%t Select[Range[0,100],aQ]

%Y Prime indices are A324701.

%Y Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.

%Y Cf. A324694, A324695, A324696, A324697, A324698, A324699, A324702, A324703, A324704, A324705.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 10 2019