A376698 a(n) is the least k >= 0 such that the k-th iterate of the run lengths transform of A376637(n) equals 1.

0, 1, 2, 3, 3, 2, 4, 4, 4, 4, 5, 3, 5, 5, 3, 5, 5, 6, 5, 6, 6, 5, 6, 5, 4, 4, 4, 4, 6, 7, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 7, 6, 6, 7, 7, 6, 6, 7, 5, 5, 5, 5, 5, 5, 5, 5, 7, 8, 7, 8, 7, 7, 7, 7, 8, 7, 8, 7, 7, 7, 8, 7, 8, 7, 8, 7, 7, 8, 8, 7, 7, 8, 7, 8, 7, 8, 7

Offset

1,3

Comments

For any k > 0, the value k appears 2^(k-1) times.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10048

Rémy Sigrist, PARI program

Formula

a(n) = a(A376676(n)) + 1 for any n > 1.

Example

The first terms, alongside the corresponding run lengths transforms, are:
  n   a(n)  Run lengths transforms
  --  ----  ---------------------------------
   1     0  1
   2     1  2 -> 1
   3     2  11 -> 2 -> 1
   4     3  12 -> 11 -> 2 -> 1
   5     3  21 -> 11 -> 2 -> 1
   6     2  22 -> 2 -> 1
   7     4  112 -> 21 -> 11 -> 2 -> 1
   8     4  122 -> 12 -> 11 -> 2 -> 1
   9     4  211 -> 12 -> 11 -> 2 -> 1
  10     4  221 -> 21 -> 11 -> 2 -> 1
  11     5  1121 -> 211 -> 12 -> 11 -> 2 -> 1
  12     3  1122 -> 22 -> 2 -> 1
  13     5  1211 -> 112 -> 21 -> 11 -> 2 -> 1
  14     5  2122 -> 112 -> 21 -> 11 -> 2 -> 1
  15     3  2211 -> 22 -> 2 -> 1
  16     5  2212 -> 211 -> 12 -> 11 -> 2 -> 1

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A376637, A376676.

Sequence in context: A238444 A076742 A373345 * A308284 A036465 A265339

Adjacent sequences: A376695 A376696 A376697 * A376699 A376700 A376701

Keyword

nonn

Author

Rémy Sigrist, Oct 02 2024

Status

approved