This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A095345 #19 Jan 06 2018 22:13:08 %S A095345 1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,3, %T A095345 1,3,1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,3, %U A095345 1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,3,1 %N A095345 a(n) is the length of the n-th run in A095346. %C A095345 This is the first sequence reached in the infinite process described in the A066983 comment line. %C A095345 (a(n)) is a morphic sequence, i.e., a letter to letter projection of a fixed point of a morphism. The morphism is 1->121,2->3,1,3->313. The fixed point is the fixed point 121312131312... starting with 1. The letter-to-letter map is 1->1, 2->1, 3->3. See also the comments in A108103. - _Michel Dekking_, Jan 06 2018 %D A095345 F. M. Dekking: "What is the long range order in the Kolakoski sequence?" in: The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer, Dordrecht (1997), pp. 115-125. %F A095345 a(n)=3 if n=2*ceiling(k*phi) for some k where phi=(1+sqrt(5))/2, otherwise a(n)=1. [_Benoit Cloitre_, Mar 02 2009] %e A095345 A095346 begins: 3,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,... and length or runs of 3's and 1's are 1,1,1,3,1,1,1,3,1,3,... %Y A095345 Cf. A064353, A095343, A095344, A095346, A108103. %K A095345 nonn %O A095345 1,4 %A A095345 _Benoit Cloitre_, Jun 03 2004