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Search: id:A001083
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| A001083 |
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Length of one version of Kolakoski sequence {A000002(i)} at n-th growth stage. |
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+0
3
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| 1, 2, 2, 3, 5, 7, 10, 15, 23, 34, 50, 75, 113, 170, 255, 382, 574, 863, 1293, 1937, 2903, 4353, 6526, 9789, 14688, 22029, 33051, 49577, 74379, 111580, 167388, 251090, 376631, 564932, 847376, 1271059, 1906628, 2859984
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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Conjecture : a(n) is asymptotic to c*(3/2)^n where c=0.5819.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 01 2004
for n>=1 a(n+2)=S^n(2) where S(n)=A054353(n) and S^k(2)=S(S^(k-1)(2)) [From Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 24 2009]
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EXAMPLE
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/* generate sequence of sequences by recursion using next1() ( origin 1 ) */ v=[2]; for(n=1,8,p1(v); print1(" -> "); v=next1(v))
2 -> 11 -> 12 -> 122 -> 12211 -> 1221121 -> 1221121221 -> 122112122122112 ->
v=[2]; for(n=1,8,print1(length(v)); print1(","); v=next1(v)) gives: 1,2,2,3,5,7,10,15,
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PROGRAM
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(PARI) /* generate sequence starting at 1 given run length sequence */ next1(v)=local(w); w=[]; for(n=1, length(v), for(i=1, v[n], w=concat(w, 2-n%2))); w
/* print a number or sequence recursively with no commas */ p1(v)=if(type(v)!="t_VEC", print1(v), for(n=1, length(v), p1(v[n])))
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CROSSREFS
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Cf. A000002, A042942.
Sequence in context: A077075 A058278 A097333 this_sequence A120412 A022864 A039894
Adjacent sequences: A001080 A001081 A001082 this_sequence A001084 A001085 A001086
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Corrected by and better description from Michael Somos, May 05 2000.
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