A060586 - OEIS

%I #6 Dec 11 2020 18:43:51

%S 0,1,1,3,3,2,3,2,3,7,6,7,6,7,7,5,5,4,7,7,6,5,4,5,6,7,7,15,15,14,13,12,

%T 13,14,15,15,12,13,13,15,15,14,15,14,15,11,10,11,10,11,11,9,9,8,15,14,

%U 15,14,15,15,13,13,12,11,11,10,9,8,9,10,11,11,12,13,13,15,15,14,15,14

%N Minimum number of moves required to reach position n starting from 0 in Tower of Hanoi (with three pegs: 0,1,2), where with position n written in base 3, 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.

%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>

%F a(n) = A060585(A060583(n)).

%e a(46) = 10 since 46 written in base 3 is 1201 (i.e. with the smallest and fourth smallest disks on the first peg, the third smallest disk on the second peg and the second smallest and any other disks on the zeroth peg) and the optimal moves starting from position 0 go through positions 2, 12, 11, 211, 210, 220, 222, 1222, 1220, 1210 taking ten moves.

%Y k appears A001316(k) times in the sequence.

%Y Cf. A001511, A055661, A055662.

%K base,nice,nonn

%O 0,4

%A _Henry Bottomley_, Apr 04 2001