A324699 Lexicographically earliest sequence of positive integers whose prime indices minus 1 already belong to the sequence.

1, 3, 7, 9, 19, 21, 27, 29, 49, 57, 63, 71, 79, 81, 87, 107, 113, 133, 147, 171, 189, 203, 213, 229, 237, 243, 261, 271, 311, 321, 339, 343, 359, 361, 399, 409, 421, 441, 457, 497, 513, 551, 553, 567, 593, 609, 619, 639, 687, 711, 729, 749, 757, 783, 791, 813

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..56.

Formula

a(n) = A306719(n) - 1.

Example

The sequence of terms together with their prime indices begins:
    1: {}
    3: {2}
    7: {4}
    9: {2,2}
   19: {8}
   21: {2,4}
   27: {2,2,2}
   29: {10}
   49: {4,4}
   57: {2,8}
   63: {2,2,4}
   71: {20}
   79: {22}
   81: {2,2,2,2}
   87: {2,10}
  107: {28}
  113: {30}
  133: {4,8}
  147: {2,4,4}
  171: {2,2,8}
  189: {2,2,2,4}

Mathematica

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

Crossrefs

Prime indices are A306719.

Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360, A306719.

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

Sequence in context: A031273 A140118 A191106 * A110674 A003528 A032913

Adjacent sequences: A324696 A324697 A324698 * A324700 A324701 A324702

Keyword

nonn

Author

Gus Wiseman, Mar 10 2019

Status

approved