The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306527 Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step. 1
1, 8, 11, 2, 5, 10, 7, 4, 9, 16, 3, 6, 13, 22, 35, 18, 21, 12, 15, 26, 23, 14, 25, 38, 55, 20, 17, 32, 47, 70, 31, 34, 49, 30, 19, 36, 53, 50, 69, 46, 93, 48, 29, 68, 95, 72, 33, 54, 37, 24, 27, 42, 39, 56, 77, 52, 71, 74, 97, 100, 51, 76, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The half-infinite board is numbered from square 1 as follows:
.
| | | | | | | |
--+-------+-------+-------+-------+-------+-------+-------+--
| | | | | | | |
| 25 . . .24 . . .23 . . .22 . . .21 . . .20 . . .19 |
| . | | | | | | . |
--+---.---+-------+-------+-------+-------+-------+---.---+--
| . | | | | | | . |
| 26 | 13 . . .12 . . .11 . . .10 . . . 9 | 18 |
| . | . | | | | . | . |
--+---.---+---.---+-------+-------+-------+---.---+---.---+--
| . | . | | | | . | . |
| 27 | 14 | 5 . . . 4 . . . 3 | 8 | 17 |
| . | . | . | | . | . | . |
--+---.---+---.---+---.---+-------+---.---+---.---+---.---+--
| . | . | . | | . | . | . |
| 28 | 15 | 6 | 1 | 2 | 7 | 16 |
| | | | | | | |
--+-------+-------+-------+-------+-------+-------+-------+--
.
The knight begins at square 1. This is a finite sequence: after 326 steps square 562 is reached after which all squares within one knight move have been visited.
LINKS
Scott R. Shannon, Image showing the knight path. The green dot is the starting square 1, the red dot is the end square 562. 4 Blue dots have been added around the final square to show all available positions have been visited.
N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019)
CROSSREFS
Sequence in context: A256877 A222299 A070478 * A347306 A109596 A164801
KEYWORD
nonn,fini,full
AUTHOR
Scott R. Shannon, Feb 21 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 22 19:06 EDT 2024. Contains 372758 sequences. (Running on oeis4.)