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

1,2

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A321696

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000002, A001462, A321695.

Sequence in context: A116452 A219966 A103958 * A321020 A204260 A122923

Adjacent sequences: A321693 A321694 A321695 * A321697 A321698 A321699

Keyword

nonn

Author

Rémy Sigrist, Nov 18 2018

Status

approved