The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360360 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A360360

Given a deck of colored cards, move the top card below the bottom-most card of the same color, with one other card between them. (If the top and bottom cards have the same color, the top card is moved to the bottom of the deck; if there is no other card of the same color, the top card is moved one step down in the deck.) a(n) is the maximum, over all initial color configurations of a deck of n cards, of the length of the eventual cycle when repeatedly applying this move.
(history; published version)

#13 by N. J. A. Sloane at Sun Feb 26 20:08:49 EST 2023

STATUS

proposed

approved

#12 by Pontus von Brömssen at Thu Feb 16 13:37:48 EST 2023

STATUS

editing

proposed

Discussion

Thu Feb 16

13:38

Pontus von Brömssen: My -> Maybe.

#11 by Pontus von Brömssen at Thu Feb 16 13:37:06 EST 2023

NAME

Given a deck of colored cards, move the top card below the bottom-most card of the same color, with one other card between them. (If the top and bottom cards have the same color, the top card is moved to the bottom of the deck; if there is no other card of the same color, the top card is moved one step down in the deck.) a(n) is the maximum cycle , over all initial color configurations of a deck of n cards, of the length obtained of the eventual cycle when repeatedly applying this move to a deck of n cards.

STATUS

proposed

editing

Discussion

Thu Feb 16

13:37

Pontus von Brömssen: My this also makes it a bit clearer?

#10 by Pontus von Brömssen at Thu Feb 16 13:31:44 EST 2023

STATUS

editing

proposed

#9 by Pontus von Brömssen at Thu Feb 16 13:29:53 EST 2023

COMMENTS

Cards of the same color are considered identical. There can be any number of different colors.

STATUS

proposed

editing

Discussion

Thu Feb 16

13:31

Pontus von Brömssen: Yes, but I prefer to phrase it like this, not to give the impression that there were any kind of restriction on the number of colours.

#8 by Pontus von Brömssen at Sun Feb 12 10:27:11 EST 2023

STATUS

editing

proposed

Discussion

Thu Feb 16

12:53

Andrew Howroyd: Perhaps add a comment: The number of different colors in the deck can be up to n.

#7 by Pontus von Brömssen at Sun Feb 12 10:26:59 EST 2023

NAME

Given a deck of colored cards, move the top card below the bottom-most card of the same color, with one other card between them. (If the top and bottom card cards have the same color, the top card is moved to the bottom of the deck; if there is no other card of the same color, the top card is moved one step down in the deck.) a(n) is the maximum cycle length obtained when repeatedly applying this move to a deck of n cards.

STATUS

proposed

editing

#6 by N. J. A. Sloane at Sun Feb 12 10:11:37 EST 2023

STATUS

editing

proposed

Discussion

Sun Feb 12

10:25

Pontus von Brömssen: There can be any number of colours. (But there are only n cards, so more than n colours will never occur.)

#5 by N. J. A. Sloane at Sun Feb 12 10:09:32 EST 2023

COMMENTS

Apparently, the lengths of all cycles (not only just the longest ones) are powers of two2.

STATUS

proposed

editing

Discussion

Sun Feb 12

10:11

N. J. A. Sloane: I made a few small edits. But what does "colored" mean?  I'm guessing there are 4 colors, is that right?

#4 by Pontus von Brömssen at Tue Feb 07 15:24:18 EST 2023

STATUS

editing

proposed

Discussion

Wed Feb 08

13:27

Pontus von Brömssen: I invented this "shuffle" as a child, when playing with disposed coloured punched cards that my dad brought home from work.