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Search: id:A089280
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| A089280 |
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Tower of Hanoi game: a(n) = the number of pegs occupied by already-moved disks after move #n. |
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+0
1
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| 1, 2, 1, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 2, 1, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A001511 states the disk number moved on the n-th move.
A035263 indicates the direction of the n-th move (clockwise or not).
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REFERENCES
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Gary W. Adamson in "Beyond Measure, A Guided Tour Through Nature, Myth and Number" by Jay Kappraff, World Scientific, 2002, Chapter 15, "Number: Gray Code and the Towers of Hanoi", Table 15.1, p. 341-342.
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FORMULA
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Write n in binary; count the length of each span of equal bits. (25 -> 11001 -> 2, 2, 1.) If there is one span, a(n)=1. Otherwise, ignore the first and last spans: a(n)=3 if an odd span-length remains; a(n)=2 if not.
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EXAMPLE
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a(25)=2 because after 25 moves, 2 pegs have disks (2&3, -, 1&4&5).
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CROSSREFS
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Cf. A001511, A035263.
Sequence in context: A059129 A081771 A066856 this_sequence A100661 A088696 A004738
Adjacent sequences: A089277 A089278 A089279 this_sequence A089281 A089282 A089283
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 28 2003
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Nov 15 2005
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