A321696 For any sequence f of positive integers, let g(f) be the unique Golomb-like sequence with run lengths given by f and let k(f) be the unique Kolakoski-like sequence with run lengths given by f and initial term 1; this sequence is the unique sequence f satisfying f = k(g(f)).

1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Rémy Sigrist, Nov 18 2018

Keywords

• nonn

Comments

See A321695 for the RUNS transform of this sequence and additional comments.

Examples

			We can build this sequence alongside A321695 iteratively:
- this sequence starts with 1,
- hence A321695 starts with 1, 2 (after the initial run of 1's, we have a run of 2's),
- hence this sequence starts with 1, 2, 2, 1, 1, 2 (after the second run of 1's, we have a run of 2's),
- hence A321695 starts with 1, 2, 2, 3, 3, 4, 5, 6, 6, 7,
- hence this sequence starts with 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1,
- etc.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A321696

Crossrefs

Cf. A000002, A001462, A321695.

Programs

PARI

See Links section.