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

Author

Henry Bottomley, Apr 03 2001

Keywords

• easy
• nonn

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

Examples

			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,...
		

Links

• 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

Crossrefs

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

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).