A060571 Tower of Hanoi: the optimal way to move an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1 is on move n to move disk A001511 from peg A060571 (here) to peg A060572.

0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 0, 2, 1, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 1

Offset

1,5

Comments

a(n) is equal to a(2n) with the 1's and 2s reversed, thus a(n) = a(4n). - Donald Sampson (marsquo(AT)hotmail.com), Dec 01 2003

Links

Table of n, a(n) for n=1..105.

J.-P. Allouche, D. Astoorian, J. Randall, and J. Shallit, Morphisms, squarefree strings, and the Tower of Hanoi puzzle, Amer. Math. Monthly 101 (1994), 651-658.

Index entries for sequences related to Towers of Hanoi

Formula

If n>2^A001511(n) then a(n)=a(n-2^A001511(n))-(-1)^A001511(n) mod 3 =A060572(n-2^A001511(n)), otherwise a(k)=0. Also A001511(n)-th digit from right of A055662(n-1).

Example

Start by moving first disk from peg 0 (to peg 1), second disk from peg 0 (to peg 2), first disk form peg 1 (to peg 2), etc. so sequence starts 0,0,1,...

Crossrefs

Cf. A001511, A055662, A060572, A060573, A060574, A060575.

Sequence in context: A295335 A227838 A050605 * A131555 A373607 A293209

Adjacent sequences: A060568 A060569 A060570 * A060572 A060573 A060574

Keyword

easy,nonn

Author

Henry Bottomley, Apr 03 2001

Status

approved