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

1,2

Links

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

Index entries for sequences related to Towers of Hanoi

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.

Example

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.

Crossrefs

Cf. A101607.

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

Sequence in context: A350651 A275832 A237839 * A102853 A304099 A293390

Adjacent sequences: A101605 A101606 A101607 * A101609 A101610 A101611

Keyword

nonn,easy

Author

Ralf Stephan, Dec 09 2004

Status

approved