A321020 - OEIS

%I #23 Feb 27 2020 23:22:31

%S 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,

%T 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,

%U 2,1,1,1,1,1,1,1,2,2,2,2,2,2,2,1

%N 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.

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

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

%C 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.

%H Rémy Sigrist, <a href="/A321020/b321020.txt">Table of n, a(n) for n = 1..25000</a>

%H N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence)

%o (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

%Y Cf. A000002, A001462, A156253.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 11 2018