A328794 Squares visited by a knight moving on a binary numbered single-digit square-spiral board where the knight moves to the smallest numbered unvisited square; the minimum distance from the origin is used if the square numbers are equal; the smallest spiral number ordering is used if the distances are equal.

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0

Offset

0

Comments

This is a variation of sequence A326918 where, instead of using single digits of the base-10 numbers to number the spiral, single digits of the binary numbers are used. Otherwise the same rules to decide the square the knight leaps to apply.

The sequence is finite. After 376 steps a square with the number 1 (standard spiral number = 320) is visited, after which all neighboring squares have been visited.

Links

Scott R. Shannon, Table of n, a(n) for n = 0..376

Scott R. Shannon, Image showing the 376 steps of the knight's path. The starting square is shown in green, and final square in red, and the eight blocking squares in blue. The yellow squares are where the next step was decided from two tied squares by choosing the lowest standard spiral number.

N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Example

The squares are numbered using single digits of the binary-number spiral number ordering as:
                                .
                                .
    0---1---1---1---1---0---1   1
    |                       |   |
    0   1---1---0---1---1   0   0
    |   |               |   |   |
    1   1   1---0---1   1   1   0
    |   |   |       |   |   |   |
    1   1   1   0---1   0   0   0
    |   |   |           |   |   |
    0   0   1---0---0---1   1   0
    |   |                   |   |
    1   0---0---1---0---0---1   1
    |                           |
    1---1---1---0---1---1---1---1
If the knight has a choice of two or more squares in this spiral with the same number which also have the same distance from the origin, then the square with the minimum standard spiral number, as shown in A316667, is chosen.

Crossrefs

Cf. A326918, A316667, A326413, A326916.

Sequence in context: A204547 A072609 A185012 * A185706 A358759 A025455

Adjacent sequences: A328791 A328792 A328793 * A328795 A328796 A328797

Keyword

nonn,fini,full,walk

Author

Scott R. Shannon, Oct 27 2019

Status

approved