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

0, 2, 4, 5, 8, 10, 11, 13, 16, 20, 22, 23, 25, 26, 31, 32, 37, 40, 43, 44, 46, 50, 52, 55, 59, 62, 64, 65, 73, 74, 80, 83, 86, 88, 89, 92, 100, 101, 103, 104, 110, 115, 118, 121, 124, 125, 128, 130, 131, 137, 143, 146, 148, 155, 160, 163, 166, 169, 172, 176

Offset

1,2

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.

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

The sequence of terms together with their prime indices begins:
   0
   2: {1}
   4: {1,1}
   5: {3}
   8: {1,1,1}
  10: {1,3}
  11: {5}
  13: {6}
  16: {1,1,1,1}
  20: {1,1,3}
  22: {1,5}
  23: {9}
  25: {3,3}
  26: {1,6}
  31: {11}
  32: {1,1,1,1,1}
  37: {12}
  40: {1,1,1,3}
  43: {14}
  44: {1,1,5}

Mathematica

aQ[n_]:=Switch[n, 0, True, 1, False, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]-1]]];
Select[Range[0, 100], aQ]

Crossrefs

Prime indices are A324701.

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

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

Sequence in context: A131396 A131391 A185392 * A191987 A138007 A284880

Adjacent sequences: A324697 A324698 A324699 * A324701 A324702 A324703

Keyword

nonn

Author

Gus Wiseman, Mar 10 2019

Status

approved