A060592 Square table by antidiagonals of minimum number of moves between two positions in the Tower of Hanoi (with three pegs: 0,1,2), where with position n written in base 3, xyz means smallest disk is on peg z, second smallest is on peg y, third smallest on peg x, etc. and leading zeros indicate largest disks are all on peg 0.

0, 1, 1, 1, 0, 1, 3, 1, 1, 3, 3, 3, 0, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 0, 2, 2, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 1, 3, 1, 0, 1, 3, 1, 3, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 6, 3, 2, 2, 0, 2, 2, 3, 6, 6, 7, 5, 7, 2, 3, 2, 2, 3, 2, 7, 5, 7, 6, 6, 6, 6, 3, 3, 0, 3, 3, 6, 6, 6, 6, 7, 5, 7, 5, 5, 3, 1, 1, 3, 5, 5, 7, 5, 7

Offset

0,7

Links

Table of n, a(n) for n=0..104.

Henry Bottomley, Graph of positions and possible routes on a Sierpinski triangle

Index entries for sequences related to Towers of Hanoi

Example

T(4,9)=5 since 4 and 9 written in base 3 are 11 and 100, i.e. the starting position has the first and second disks on peg 1 and the others on peg 0, while the end position has the third disk on peg 1 and the others on peg 0; the five optimal moves between these positions are: move the third disk to peg 2, then the first to peg 2, the second to peg 0, the first to peg 0 and finally the third to peg 1.

Crossrefs

Cf. A001511, A007798, A055661, A055662.

Sequence in context: A278509 A094782 A035666 * A080426 A230293 A133116

Adjacent sequences: A060589 A060590 A060591 * A060593 A060594 A060595

Keyword

nonn,tabl

Author

Henry Bottomley, Apr 06 2001

Status

approved