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%I #18 Sep 04 2021 05:53:15
%S 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,
%T 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,
%U 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
%N 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.
%C 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
%H J.-P. Allouche, D. Astoorian, J. Randall, and J. Shallit, <a href="http://www.jstor.org/stable/2974693">Morphisms, squarefree strings, and the Tower of Hanoi puzzle</a>, Amer. Math. Monthly 101 (1994), 651-658.
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F 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).
%e 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,...
%Y Cf. A001511, A055662, A060572, A060573, A060574, A060575.
%K easy,nonn
%O 1,5
%A _Henry Bottomley_, Apr 03 2001
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