%I #22 Dec 03 2021 17:23:48
%S 0,1,21,22,122,120,110,111,2111,2112,2102,2100,2200,2201,2221,2222,
%T 12222,12220,12210,12211,12011,12012,12002,12000,11000,11001,11021,
%U 11022,11122,11120,11110,11111,211111,211112,211102,211100,211200
%N Successive positions in Tower of Hanoi (with three pegs {0,1,2}) where xyz means smallest disk is on peg z, second smallest is on peg y, third smallest on peg x, etc. and leading zeros indicate largest disks are all on peg 0.
%C Optimal for moving an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1.
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F a(n) = Sum_{j=0..floor(log_2(n))} 10^j * (floor((n/2^j + 1)/2)*(-1)^j mod 3).
%t a[n_]:=Sum[10^j*(Mod[(-1)^j*Floor[(n/2^j + 1)/2],3]), {j,0,Floor[Log2[n]]}]; Array[a, 70, 0] (* _Stefano Spezia_, Oct 27 2018 *)
%Y Cf. A001511, A055661.
%Y Cf. A060572.
%K nonn
%O 0,3
%A _Henry Bottomley_, Jun 06 2000