A324698 Lexicographically earliest sequence containing 2 and all numbers > 1 whose prime indices already belong to the sequence.

2, 3, 5, 9, 11, 15, 23, 25, 27, 31, 33, 45, 47, 55, 69, 75, 81, 83, 93, 97, 99, 103, 115, 121, 125, 127, 135, 137, 141, 155, 165, 197, 207, 211, 225, 235, 243, 249, 253, 257, 275, 279, 291, 297, 309, 341, 345, 347, 363, 375, 379, 381, 405, 411, 415, 419, 423

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.

Links

Table of n, a(n) for n=1..57.

Example

The sequence of terms together with their prime indices begins:
   2: {1}
   3: {2}
   5: {3}
   9: {2,2}
  11: {5}
  15: {2,3}
  23: {9}
  25: {3,3}
  27: {2,2,2}
  31: {11}
  33: {2,5}
  45: {2,2,3}
  47: {15}
  55: {3,5}
  69: {2,9}
  75: {2,3,3}
  81: {2,2,2,2}
  83: {23}
  93: {2,11}
  97: {25}
  99: {2,2,5}

Mathematica

aQ[n_]:=Switch[n, 1, False, 2, True, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]];
Select[Range[100], aQ]

Crossrefs

Complement of A324704.

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

Cf. A324694, A324695, A324696, A324697, A324699, A324700, A324701, A324702, A324703, A324705.

Sequence in context: A102940 A157049 A195668 * A059042 A157604 A238657

Adjacent sequences: A324695 A324696 A324697 * A324699 A324700 A324701

Keyword

nonn

Author

Gus Wiseman, Mar 10 2019

Status

approved