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 A073645 a(1)=2 and, for all n>=1, a(n) is the length of the n-th run of increasing consecutive integers with each run after the first starting with 1. 1
 2, 3, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Unlike the Kolakoski sequence A000002 which is also based on run-lengths and has an unpredictable, complex dynamic behavior, this sequence appears to be completely described by an easily evaluated formula. Removing the initial 2 it remains the fixed point of the morphism: 3-->123, 2-->12, 1->1. Thus the given formulas are exact. Moreover the sequence of length of runs of 1s is given by A004736. - Benoit Cloitre, Feb 18 2009 LINKS FORMULA Conjecture: Let P(k)=1 + k/3 + k^2/2 + k^3/6. Then a(n)=3 if n=P(k) for some k, a(n)=2 if P(k-1)

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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)