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

0,2

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A062039 A352866 A352883 * A101229 A057176 A194671

Adjacent sequences: A035489 A035490 A035491 * A035493 A035494 A035495

Keyword

nonn

Author

Wouter Meeussen

Status

approved