A391638 Binary encoding of the disks missing from pin 1, after n moves, when moving infinitely many disks in the Tower of Hanoi starting from pin 1, via the optimal algorithm.

0, 1, 3, 3, 7, 6, 6, 7, 15, 15, 13, 12, 12, 13, 15, 15, 31, 30, 30, 31, 27, 27, 25, 24, 24, 25, 27, 27, 31, 30, 30, 31, 63, 63, 61, 60, 60, 61, 63, 63, 55, 54, 54, 55, 51, 51, 49, 48, 48, 49, 51, 51, 55, 54, 54, 55, 63, 63, 61, 60, 60, 61, 63, 63, 127, 126

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 2. Initially infinitely many disks are on pin 0. 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) = 3, disks 0 and 1 are missing from pin 1 after 3 moves.

The number k appears in this sequence if and only if it is in A295897.

Links

Table of n, a(n) for n=0..65.

Formula

a(n) = A392654(n) + A392655(n).

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) = 3, disks 0 and 1 are missing from pin 1 after 3 moves.

Crossrefs

Cf. A295897, A392654, A392655.

Sequence in context: A290418 A200690 A045773 * A256700 A175039 A222405

Adjacent sequences: A391635 A391636 A391637 * A391639 A391640 A391641

Keyword

nonn

Author

Jeffrey Shallit, Jan 18 2026

Status

approved