The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343530

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A343530

Number of steps before being trapped for a knight moving on a square-spiral base-n numbered board when stepping to the closest unvisited square which contains a number that shares no digit with the number of the current square. If two or more such squares are the same distance away the one with the smaller number is chosen.
(history; published version)

#37 by Susanna Cuyler at Thu Jun 17 13:58:53 EDT 2021

STATUS

reviewed

approved

#36 by Michel Marcus at Thu Jun 17 01:06:33 EDT 2021

STATUS

proposed

reviewed

#35 by Rémy Sigrist at Thu Jun 17 00:54:28 EDT 2021

STATUS

editing

proposed

#34 by Rémy Sigrist at Thu Jun 17 00:53:55 EDT 2021

LINKS

Rémy Sigrist, <a href="/A343530/b343530.txt">Table of n, a(n) for n = 2..3500</a>

STATUS

approved

editing

Discussion

Thu Jun 17

00:54

Rémy Sigrist: added b-file

#33 by N. J. A. Sloane at Wed Jun 16 21:01:51 EDT 2021

STATUS

proposed

approved

#32 by Jon E. Schoenfield at Wed Jun 16 20:29:36 EDT 2021

STATUS

editing

proposed

Discussion

Wed Jun 16

20:38

Jon E. Schoenfield: Unless I'm badly mistaken, a term like "base-3" should be hyphenated when it functions as an adjective, but it should not be hyphenated when it functions as a noun.  For example, in places like "on a base-3 numbered board", "base-3" functions as an adjective (modifying "numbered board"), so it gets a hyphen.  But in places like "The board in base 10", "base 10" functions as a noun (the object of the preposition "in"), so it shouldn't be hyphenated.

21:01

N. J. A. Sloane: Jon is right, as always

#31 by Jon E. Schoenfield at Wed Jun 16 20:29:34 EDT 2021

LINKS

Scott R. Shannon, <a href="/A343530/a343530.png">Image of the path for a(4) = 12</a>. In this and other images the starting square is highlighted in white, the visited squares, numbered in base- n, in yellow, the final square in red, while the path is colored across the spectrum to show the relative step ordering.

EXAMPLE

The board in base- 10 is numbered with the square spiral:

18 5---4---3 12 29

19 6 1---2 11 28

20 7---8---9--10 27

a(3) = 1 as on a base-3 numbered board there are two squares the knight can step to which do not contain a 1 digit - - the square squares numbered 200_3 = 18 and 220_3 = 24. The knight steps to 200_3 as it is the lowest numbered square, but after that there are no surrounding unvisited squares the knight can step to which do not contain the digit 0 or 2.

STATUS

proposed

editing

#30 by Rémy Sigrist at Wed Jun 16 10:54:28 EDT 2021

STATUS

editing

proposed

#29 by Rémy Sigrist at Wed Jun 16 10:52:48 EDT 2021

FORMULA

a(n) = 2015 for any n >= 2979. - Rémy Sigrist, Jun 16 2021

STATUS

proposed

editing

Discussion

Wed Jun 16

10:54

Rémy Sigrist: the sequence is eventually constant

#28 by Rémy Sigrist at Wed Jun 16 07:12:21 EDT 2021

STATUS

editing

proposed

Discussion

Wed Jun 16

07:15

Rémy Sigrist: added program (not b-file)