Search: id:A001083 Results 1-1 of 1 results found. %I A001083 %S A001083 1,2,2,3,5,7,10,15,23,34,50,75,113,170,255,382,574,863,1293, %T A001083 1937,2903,4353,6526,9789,14688,22029,33051,49577,74379,111580, %U A001083 167388,251090,376631,564932,847376,1271059,1906628,2859984 %N A001083 Length of one version of Kolakoski sequence {A000002(i)} at n-th growth stage. %H A001083 Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. %F A001083 Conjecture : a(n) is asymptotic to c*(3/2)^n where c=0.5819.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 01 2004 %F A001083 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] %e A001083 /* generate sequence of sequences by recursion using next1() ( origin 1 ) */ v=[2]; for(n=1,8,p1(v); print1(" -> "); v=next1(v)) %e A001083 2 -> 11 -> 12 -> 122 -> 12211 -> 1221121 -> 1221121221 -> 122112122122112 -> %e A001083 v=[2]; for(n=1,8,print1(length(v)); print1(","); v=next1(v)) gives: 1, 2,2,3,5,7,10,15, %o A001083 (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 %o A001083 /* 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]))) %Y A001083 Cf. A000002, A042942. %Y A001083 Sequence in context: A077075 A058278 A097333 this_sequence A120412 A022864 A039894 %Y A001083 Adjacent sequences: A001080 A001081 A001082 this_sequence A001084 A001085 A001086 %K A001083 nonn %O A001083 1,2 %A A001083 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com) %E A001083 Corrected by and better description from Michael Somos, May 05 2000. Search completed in 0.001 seconds