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

2, 5, 13, 25, 43, 65, 101, 125, 169, 193, 215, 317, 325, 505, 557, 559, 625, 701, 845, 965, 1013, 1075, 1181, 1313, 1321, 1585, 1625, 1849, 2111, 2161, 2197, 2509, 2525, 2785, 2795, 3125, 3505, 3617, 4049, 4057, 4121, 4225, 4343, 4639, 4825, 5065, 5297, 5375

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.

Also 2 and numbers whose prime indices belong to A324703.

Links

Table of n, a(n) for n=1..48.

Formula

a(n) = A324703(n) - 1.

Example

The sequence of terms together with their prime indices begins:
    2: {1}
    5: {3}
   13: {6}
   25: {3,3}
   43: {14}
   65: {3,6}
  101: {26}
  125: {3,3,3}
  169: {6,6}
  193: {44}
  215: {3,14}
  317: {66}
  325: {3,3,6}
  505: {3,26}
  557: {102}
  559: {6,14}
  625: {3,3,3,3}
  701: {126}
  845: {3,6,6}
  965: {3,44}

Mathematica

aQ[n_]:=Switch[n, 0, False, 1, False, 2, True, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]-1]]];
Select[Range[100], aQ]

Crossrefs

Prime indices > 1 are A324703.

Cf. A000002, A000720, A001222, A001462, A007097, A045965, A055396, A061395, A064989, A079000, A079254, A109298, A112798, A276625, A277098, A304360.

Cf. A324694, A324695, A324696, A324697, A324698, A324699, A324700, A324701, A324704, A324705.

Sequence in context: A362105 A309230 A048871 * A072921 A369714 A289529

Adjacent sequences: A324699 A324700 A324701 * A324703 A324704 A324705

Keyword

nonn

Author

Gus Wiseman, Mar 11 2019

Status

approved