The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001083 Length of one version of Kolakoski sequence {A000002(i)} at n-th growth stage. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..38. Konstantinos Lambropoulos and Constantinos Simserides, Spectral, localization and charge transport properties of periodic, aperiodic and random binary sequences, arXiv:1808.04764 [cond-mat.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+3) = S^n(2) where S(n) = A054353(n) and S^k(2) = S(S^(k-1)(2)). - Benoit Cloitre, Feb 24 2009 [adjusted to match sequence offset by Jon Maiga, Jul 27 2022] Equivalently, a(n) = A054353(a(n-1)) for n>3. - Jon Maiga, Jul 10 2022 EXAMPLE /* generate sequence of sequences by recursion using next1() ( origin 1 ) */ v=; for(n=1,8,p1(v); print1(" -> "); v=next1(v)) 2 -> 11 -> 12 -> 122 -> 12211 -> 1221121 -> 1221121221 -> 122112122122112 -> v=; 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, 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]))) CROSSREFS Cf. A000002, A042942, A054353. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 03:08 EST 2023. Contains 367452 sequences. (Running on oeis4.)