cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054349 Successive generations of the variant of the Kolakoski sequence described in A042942.

This page as a plain text file.
%I A054349 #20 Apr 13 2020 07:13:33
%S A054349 2,22,2211,221121,221121221,22112122122112,2211212212211211221211,
%T A054349 221121221221121122121121221121121,
%U A054349 2211212212211211221211212211211212212211212212112
%N A054349 Successive generations of the variant of the Kolakoski sequence described in A042942.
%C A054349 For n >= 0, let f_1(n) be the number of 1's in a(n) (sequence begins: 0, 0, 2, 3, 4, 6, 11, 17, 24, ...) and f_2(n) be the number of 2's (sequence begins: 1, 2, 2, 3, 5, 8, 11, 16, 25, ...). Then there is a simple relation between f_1 and f_2, namely: f_1(n) = 1 - f_2(n) + f_2(n-1) + f_2(n-2) + ... + f_2(0). i.e. f_1(7) = 17 and 1 - f_2(7) + f_2(6) + ... + f_2(0) = 1 - 16 + 11 + 8 + 5 + 3 + 2 + 2 + 1 = 17. - _Benoit Cloitre_, Oct 11 2005
%H A054349 Bertran Steinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.html">A Recursive Formula for the Kolakoski Sequence A000002</a>, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.
%Y A054349 Cf. A000002, A054348, A054350, A054351, A111123, A111124.
%Y A054349 Word lengths give A042942.
%K A054349 nonn,easy
%O A054349 0,1
%A A054349 _N. J. A. Sloane_, May 07 2000
%E A054349 More terms from _David Wasserman_, Mar 04 2002