A089280 Tower of Hanoi game: a(n) is the number of pegs occupied by already-moved disks after move #n.

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

Offset

1,2

Comments

A001511 states the disk number moved on the n-th move.

A035263 indicates the direction of the n-th move (clockwise or not).

References

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.

Links

Table of n, a(n) for n=1..102.

Index entries for sequences related to Towers of Hanoi

Formula

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.

Example

a(25)=2 because after 25 moves, 2 pegs have disks (2&3, -, 1&4&5).

Crossrefs

Cf. A001511, A035263.

Sequence in context: A081771 A338170 A066856 * A246960 A285200 A308567

Adjacent sequences: A089277 A089278 A089279 * A089281 A089282 A089283

Keyword

nonn

Author

Gary W. Adamson, Oct 28 2003

Extensions

Edited by Don Reble, Nov 15 2005

Status

approved