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A321512 Characteristic function of the reverse in the shuffle (perfect faro shuffle with cut): 1 if the sequence of shuffles of n cards contains the reverse of the original order of cards, 0 if not. 1
1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

The characteristic function of A321580: 1 if in the sequence of Faro's shuffle of n cards there is at some point the exact reverse of the initial order (the cards are backwards); 0 if not.

LINKS

Table of n, a(n) for n=1..100.

Index entries for characteristic functions

EXAMPLE

For example, for n = 4, we have the following sequence of shuffles:

  c(1) = 1234 <- initial order of cards

  c(2) = 2413

  c(3) = 4321 <- here's the reverse of c(1)

  c(4) = 3142

  c(5) = 1234

Hence the characteristic function at n = 4 is 1.

For n = 5,

  c(1) = 12345

  c(2) = 24135

  c(3) = 43215

  c(4) = 31425

  c(5) = 12345

Observe that for n = 5, there's no 54321 in the c(i) sequence, so the characteristic function at n = 5 is 0.

PROG

(Python3)

for n in range(1, 101):

   cards = [i for i in range(1, n + 1)]

   reverse = cards[::-1]

     shuffled = cards.copy()

   reversein = False

   for i in range(n):

      evens = shuffled[1::2]

      odds = shuffled[0::2]

      shuffled = evens + odds

        if shuffled == reverse:

         reversein = True

   print(n, int(reversein))

CROSSREFS

Cf. A024222, A123320, A049206.

Sequence in context: A154269 A036987 A181101 * A297054 A266459 A214509

Adjacent sequences:  A321509 A321510 A321511 * A321513 A321514 A321515

KEYWORD

nonn

AUTHOR

Pedro Menezes, Nov 11 2018

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)