A377648 Parse Golomb's sequence (A001462) into distinct phrases [1], [2], [2, 3], [3], [4], [4, 4], [5], [5, 5], ...; a(n) is the length of n-th phrase.

1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 3

Offset: 1

Author

Rémy Sigrist, Nov 03 2024

Keywords

• nonn

Comments

For any w > 0, we have some k such that a(k) = 1, a(k+1) = 2, ..., a(k+w-1) = w.

Examples

			The first terms, alongside the corresponding phrases, are:
  n   a(n)  Corresponding phrases
  --  ----  ---------------------
   1     1  1
   2     1  2
   3     2  2, 3
   4     1  3
   5     1  4
   6     2  4, 4
   7     1  5
   8     2  5, 5
   9     1  6
  10     2  6, 6
  11     2  6, 7
  12     1  7
  13     2  7, 7
  14     1  8
  15     2  8, 8
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Ordinal transform of the first 100000 terms
• Rémy Sigrist, PARI program

Crossrefs

See A187199 for a similar sequence.

Cf. A001462.

Programs

PARI

\\ See Links section.