A035493 Order in which new cards appear on top of deck in Guy's shuffling problem A035485.

1, 2, 3, 6, 5, 9, 4, 16, 10, 12, 14, 23, 18, 20, 17, 27, 30, 33, 38, 37, 32, 11, 19, 53, 25, 21, 34, 8, 50, 48, 46, 47, 84, 52, 31, 49, 51, 91, 61, 42, 79, 29, 26, 115, 70, 93, 109, 124, 97, 134, 111, 7, 129, 131, 157, 107, 123, 117, 96, 94, 72, 178, 86, 35, 121

Offset

1,2

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 = 1..6679

Eric Weisstein's World of Mathematics, Perfect Shuffle.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    deck = []; tops = {1}; 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
        if deck[0] not in tops: tops.add(deck[0]); yield deck[0]
print(list(islice(agen(), 65))) # Michael S. Branicky, Aug 11 2022

Crossrefs

Cf. A035485, A035490, A035491, A035492, A035494, A035500.

Sequence in context: A329564 A257011 A144652 * A363277 A070038 A328638

Adjacent sequences: A035490 A035491 A035492 * A035494 A035495 A035496

Keyword

nonn

Author

N. J. A. Sloane, Wouter Meeussen

Extensions

Extended (and corrected) by Jud McCranie

Status

approved