A321020 A hybrid of Kolakoski's sequence A000002 and Golomb's sequence A001462: if A001462(n) is odd replace it with 1, if even with 2.

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

Offset

1,2

Comments

This is A000002 rewritten so the run lengths are given by A001462.

The companion sequence, A001462 rewritten so the run lengths are given by A000002, seems to be A156253.

Note that Kolakoski's sequence A000002 and Golomb's sequence A001462 have very similar definitions, although the asymptotic behavior of A001462 is well-understood, while that of A000002 is a mystery. The asymptotic behavior of the two hybrids A156253 and A321020 might be worth investigating.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..25000

N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Prog

(PARI) a = vector(84, k, k); for (i=1, oo, for (j=1, a[i], a[n++] = i; print1 (2-(i%2) ", "); if (n==#a, break(2)))) \\ Rémy Sigrist, Nov 12 2018

Crossrefs

Cf. A000002, A001462, A156253.

Sequence in context: A219966 A103958 A321696 * A204260 A122923 A113971

Adjacent sequences: A321017 A321018 A321019 * A321021 A321022 A321023

Keyword

nonn

Author

N. J. A. Sloane, Nov 11 2018

Status

approved