A035500 Shuffles at which new cards appear on top of deck in Guy's shuffling problem A035485.

0, 1, 2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 25, 26, 28, 29, 30, 32, 33, 35, 37, 38, 39, 40, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 60, 62, 64, 65, 66, 72, 73, 76, 77, 78, 83, 84, 85, 86, 87, 88, 89, 90, 91, 94, 95, 97, 98, 99, 101, 102, 103, 104

Offset: 1

Author

N. J. A. Sloane, Wouter Meeussen

Keywords

• nonn

References

• D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," 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..10000

Crossrefs

Cf. A035485, A035493, A035501.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    deck = []; tops = {1}; yield 0
    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 n
print(list(islice(agen(), 70))) # Michael S. Branicky, Aug 11 2022

Extensions

Extended (and corrected) by Jud McCranie