A055662 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.

0, 1, 21, 22, 122, 120, 110, 111, 2111, 2112, 2102, 2100, 2200, 2201, 2221, 2222, 12222, 12220, 12210, 12211, 12011, 12012, 12002, 12000, 11000, 11001, 11021, 11022, 11122, 11120, 11110, 11111, 211111, 211112, 211102, 211100, 211200

Offset: 0

Author

Henry Bottomley, Jun 06 2000

Keywords

• nonn

Comments

Optimal for moving an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1.

Links

• Index entries for sequences related to Towers of Hanoi

Crossrefs

Cf. A001511, A055661.

Cf. A060572.

Programs

Mathematica

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 *)

Formula

a(n) = Sum_{j=0..floor(log_2(n))} 10^j * (floor((n/2^j + 1)/2)*(-1)^j mod 3).