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

Author

Rémy Sigrist, Oct 02 2024

Keywords

• nonn

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A376637, A376676.

Programs

PARI

\\ See Links section.

Formula

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