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A054349 Successive generations of the variant of the Kolakoski sequence described in A042942. 5
2, 22, 2211, 221121, 221121221, 22112122122112, 2211212212211211221211, 221121221221121122121121221121121, 2211212212211211221211212211211212212211212212112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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(1)+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

LINKS

Table of n, a(n) for n=0..8.

Bertran Steinsky, A Recursive Formula for the Kolakoski Sequence A000002, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.

CROSSREFS

Cf. A054348, A054350, A054351, A042942, A000002.

Word lengths give A042942.

Sequence in context: A104149 A113761 A319620 * A182293 A222000 A261400

Adjacent sequences:  A054346 A054347 A054348 * A054350 A054351 A054352

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 07 2000

EXTENSIONS

More terms from David Wasserman, Mar 04 2002

STATUS

approved

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Last modified February 20 04:44 EST 2020. Contains 332063 sequences. (Running on oeis4.)