

A001083


Length of one version of Kolakoski sequence {A000002(i)} at nth growth stage.


3



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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..38.
Konstantinos Lambropoulos, Constantinos Simserides, Spectral, localization and charge transport properties of periodic, aperiodic and random binary sequences, arXiv:1808.04764 [condmat.soft], 2018.
Eric Weisstein's World of Mathematics, Kolakoski Sequence


FORMULA

Conjecture : a(n) is asymptotic to c*(3/2)^n where c=0.5819....  Benoit Cloitre, Jun 01 2004
for n>=1 a(n+2)=S^n(2) where S(n)=A054353(n) and S^k(2)=S(S^(k1)(2)). [Benoit Cloitre, Feb 24 2009]


EXAMPLE

/* 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,


PROG

(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, 2n%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])))


CROSSREFS

Cf. A000002, A042942.
Sequence in context: A173693 A058278 A097333 * A173696 A120412 A022864
Adjacent sequences: A001080 A001081 A001082 * A001084 A001085 A001086


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

Corrected by and better description from Michael Somos, May 05 2000


STATUS

approved



