A101608 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.