A101608 Solution to Tower of Hanoi puzzle encoded in pairs with the moves (1,2),(2,3),(3,1),(2,1),(3,2),(1,3). The disks are moved from peg 1 to 2. For a tower of k disks use the first 2^k-1 number pairs.

1, 2, 1, 3, 2, 3, 1, 2, 3, 1, 3, 2, 1, 2, 1, 3, 2, 3, 2, 1, 3, 1, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 2, 1, 3, 1, 3, 2, 1, 2, 1, 3, 2, 3, 1, 2, 3, 1, 3, 2, 1, 2, 1, 3, 2, 3, 2, 1, 3, 1, 2, 3, 1, 2, 1, 3, 2, 3, 2, 1, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 2, 1, 3, 1, 2, 3, 1, 2, 1, 3, 2, 3

Offset: 1

Author

Ralf Stephan, Dec 09 2004

Keywords

• nonn
• easy

Examples

			The solution to the 3-disk puzzle is (1,2),(1,3),(2,3),(1,2),(3,1),(3,2),(1,2), therefore a(1) through a(7) are the same numbers in sequence.
		

Links

• Index entries for sequences related to Towers of Hanoi

Crossrefs

Cf. A101607.

If the number of disks is odd see A210243. [Y. Z. Chen, Apr 10 2012]

Formula

Recurrence: a(4n+1) = (n mod 3) + 1, a(4n+2) = (n+1 mod 3) + 1, a(4n+3) = f(a(2n+1)), a(4n+4) = f(a(2n+2)), where f(1)=1, f(2)=3, f(3)=2.