A035492 Position of card 1 after n-th shuffle in Guy's shuffling problem (A035485).

1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 7, 14, 28, 25, 17, 34, 31, 23, 5, 10, 20, 40, 31, 11, 22, 44, 31, 3, 6, 12, 24, 48, 27, 54, 35, 70, 63, 47, 13, 26, 52, 17, 34, 68, 43, 86, 75, 51, 1, 2, 4, 8, 16, 32, 64, 13, 26, 52, 104, 85, 45, 90, 51

Offset: 0

Author

Wouter Meeussen

Keywords

• nonn

References

• D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
• D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.

Links

• Lars Blomberg, Table of n, a(n) for n = 0..9999
• Eric Weisstein's World of Mathematics, Perfect Shuffle.

Crossrefs

Cf. A035485, A035490, A035491, A035493, A035494.

Programs

Mathematica

Transpose[Position[NestList[riguy, {}, 64], 1]][[2]] (* See A035490. *)

Python

from itertools import count, islice
def agen(): # generator of terms
    deck = []; yield 1
    for n in count(1):
        deck += [2*n-1, 2*n]
        first, next = deck[:n], deck[n:2*n]
        deck[0:2*n:2], deck[1:2*n:2] = next, first
        yield deck.index(1) + 1
print(list(islice(agen(), 65))) # Michael S. Branicky, Aug 11 2022