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 A078880 The sequence starting with 2 that equals its own run length sequence. 3
 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is an unsolved problem to show that the density of 1's is equal to 1/2. The sequence can be generated by starting with 22 and applying the block-substitution rules 22 -> 2211, 21 -> 221, 12 -> 211, 11 -> 21. (Lagarias) REFERENCES M. S. Keane, Ergodic theory and subshifts of finite type, Chap. 2 of T. Bedford et al., eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford, 1991, esp. p. 50. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 J.-M. Fedou, G. Fici, Some remarks on differentiable sequences and recursivity, JIS 13 (2010) # 10.3.2. FORMULA a(n) = k(n+1), where k=A000002, the Kolakoski sequence. EXAMPLE Start with 2, which generates 22 (so that the first run length is 2); then 22 generates 2211 (so that the first two run lengths are 2 and 2); then 2211 generates 221121 and so on. MATHEMATICA seed = {2, 1}; w = {}; i = 1; Do[w = Join[w, Array[seed[[Mod[i - 1, Length[seed]] + 1]] &, If[i > Length[w], seed, w][[i]]]]; i++, {n, 70}]; w (* Ivan Neretin, Apr 02 2015 *) CROSSREFS See A000002, this sequence prepended with 1, for properties, formulas, references, links, programs, etc. Sequence in context: A278387 A074293 A013949 * A000002 A074295 A236479 Adjacent sequences:  A078877 A078878 A078879 * A078881 A078882 A078883 KEYWORD nonn AUTHOR Clark Kimberling, Dec 11 2002 STATUS approved

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Last modified December 19 08:25 EST 2018. Contains 318245 sequences. (Running on oeis4.)