id:A073645 - OEIS Search Results

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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.

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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; listen)

	OFFSET	`1,1`
	COMMENT	`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.`
	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)<n<P(k) for some k and P(k)-n=m(m+1)/2 for some m, else a(n)=1.`
	EXAMPLE	`a(1)=2 requires a(2)=3 to complete the first run of length 2; a(2)=3 then requires a(3)=1, a(4)=2, and a(5)=3 to complete the second run of length 3; etc. (From Labos E.)`
	CROSSREFS	`Sequence in context: A079087 A053839 A047896 this_sequence A082846 A117373 A132677` `Adjacent sequences: A073642 A073643 A073644 this_sequence A073646 A073647 A073648`
	KEYWORD	`nonn`
	AUTHOR	`John W. Layman (layman(AT)math.vt.edu), Aug 29 2002`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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