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

0,3

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

Table of n, a(n) for n=0..36.

Index entries for sequences related to Towers of Hanoi

Formula

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

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 *)

Crossrefs

Cf. A001511, A055661.

Cf. A060572.

Sequence in context: A041906 A041904 A041908 * A041910 A041912 A041914

Adjacent sequences: A055659 A055660 A055661 * A055663 A055664 A055665

Keyword

nonn

Author

Henry Bottomley, Jun 06 2000

Status

approved