A392654 Binary-encoded contents of pin 3, after n moves, when moving infinitely many disks in the Tower of Hanoi starting from pin 1, via the optimal algorithm.

0, 0, 2, 3, 3, 2, 0, 0, 8, 9, 9, 8, 12, 12, 14, 15, 15, 14, 12, 12, 8, 9, 9, 8, 0, 0, 2, 3, 3, 2, 0, 0, 32, 33, 33, 32, 36, 36, 38, 39, 39, 38, 36, 36, 32, 33, 33, 32, 48, 48, 50, 51, 51, 50, 48, 48, 56, 57, 57, 56, 60, 60, 62, 63, 63, 62, 60, 60, 56, 57, 57

Offset

0,3

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 3. Initially infinitely many disks are on pin 0.

Links

Table of n, a(n) for n=0..70.

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, move 4 moves a disk from pin 1 to pin 2, move 5 moves a disk from pin 3 to pin 1. Since a(4) = 3, pin 2 holds disks 0 and 1 after 4 moves, and since a(5) = 2, pin 2 contains disk number 1 only.

Crossrefs

Cf. A391638, A392655.

Sequence in context: A131012 A083057 A099028 * A357521 A279645 A198197

Adjacent sequences: A392651 A392652 A392653 * A392655 A392656 A392657

Keyword

nonn

Author

Jeffrey Shallit, Jan 18 2026

Status

approved