A392655 Binary-encoded contents of pin 2, after n moves, when moving infinitely many disks in the Tower of Hanoi starting from pin 1, via the optimal algorithm.

0, 1, 1, 0, 4, 4, 6, 7, 7, 6, 4, 4, 0, 1, 1, 0, 16, 16, 18, 19, 19, 18, 16, 16, 24, 25, 25, 24, 28, 28, 30, 31, 31, 30, 28, 28, 24, 25, 25, 24, 16, 16, 18, 19, 19, 18, 16, 16, 0, 1, 1, 0, 4, 4, 6, 7, 7, 6, 4, 4, 0, 1, 1, 0, 64, 64, 66, 67, 67, 66, 64, 64, 72

Offset

0,5

Comments

Disks are numbered 0,1,2,... with the smallest numbered 0. Write a(n) in base 2; the powers 2^i appearing therein tells you what disks are on pin 2. Initially infinitely many disks are on pin 0.

The number k appears in this sequence if and only if it appears in A165404.

Links

Table of n, a(n) for n=0..72.

Example

Move 1 moves a disk from pin 1 to pin 2, move 2 moves a disk from pin 1 to pin 3, move 3 moves a disk from pin 2 to pin 3.   Since a(3) = 0, there are no disks on pin 2 after 3 moves, and since a(4) = 4, pin 2 contains disk number 2 only.

Crossrefs

Cf. A165404, A391638, A392654.

Sequence in context: A203632 A278766 A320828 * A065677 A006672 A107287

Adjacent sequences: A392652 A392653 A392654 * A392656 A392657 A392658

Keyword

nonn

Author

Jeffrey Shallit, Jan 18 2026

Status

approved