%I #11 Jan 20 2021 03:29:02
%S 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,
%T 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,
%U 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
%N 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.
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F 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.
%e 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.
%Y Cf. A101607.
%Y If the number of disks is odd see A210243. [Y. Z. Chen, Apr 10 2012]
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Dec 09 2004