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A024542 Lower bound on cumulative mean of distances between cards after n shuffles in A024222. 3

%I #8 Jul 15 2019 22:19:04

%S 0,1,1,1,1,2,2,2,2,3,3,4,4,4,4,4,4,5,6,6,6,6,7,7,8,8,8,9,9,10,7,7,8,8,

%T 11,11,12,12,12,12,12,12,11,12,14,14,15,15,16,16,14,14,17,18,17,17,15,

%U 15,19,20,20,20,13,13,13,14,22,22,22,22,23,23,18,18,24,24,25,25,26,26

%N Lower bound on cumulative mean of distances between cards after n shuffles in A024222.

%D Martin Gardner, "Card Shuffles," Mathematical Carnival, chapter 10, pages 123-138. New York: Vintage Books, 1977.

%D Tim Folger, "Shuffling Into Hyperspace," Discover, 1991 (vol 12, no 1), pages 66-67.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a024/A024542.java">Java program</a> (github)

%e a(6)=2. Without cut, after shuffle 1 (s1), order is 4 1 5 2 6 3; after s2, 2 4 6 1 3 5; after s3, 1 2 3 4 5 6. Mean distances between cards after s1 = 3.4 (17/5), s2 = 2.6 (13/5), s3 = 1 (5/5). 35/15=2.3, cumulative mean distance, so lower bound is 2. (Cuts change number of shuffles required to return cards to original order, in this case from 3 to 4.)

%Y Cf. A024222.

%K easy,nonn

%O 1,6

%A _Enoch Haga_

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)