A306719 Lexicographically earliest sequence containing 2 and all positive integers n such that the prime indices of n - 1 already belong to the sequence.

2, 4, 8, 10, 20, 22, 28, 30, 50, 58, 64, 72, 80, 82, 88, 108, 114, 134, 148, 172, 190, 204, 214, 230, 238, 244, 262, 272, 312, 322, 340, 344, 360, 362, 400, 410, 422, 442, 458, 498, 514, 552, 554, 568, 594, 610, 620, 640, 688, 712, 730, 750, 758, 784, 792, 814

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..56.

Formula

a(n) = A324699(n) + 1.

Mathematica

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

Crossrefs

Prime indices of A324699.

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

Cf. A324694, A324695, A324696, A324697, A324698, A324700, A324701, A324702, A324703, A324704, A324705.

Sequence in context: A261931 A173816 A287266 * A185400 A099942 A033092

Adjacent sequences: A306716 A306717 A306718 * A306720 A306721 A306722

Keyword

nonn

Author

Gus Wiseman, Mar 11 2019

Status

approved