A035501 Shuffles at which new record high cards appear on top of deck in Guy's shuffling problem A035485.

0, 1, 2, 4, 6, 10, 14, 19, 20, 21, 22, 30, 46, 52, 62, 72, 76, 85, 94, 120, 126, 144, 147, 169, 174, 190, 216, 221, 241, 251, 254, 273, 281, 289, 292, 300, 301, 305, 308, 323, 338, 341, 379, 382, 399, 421, 429, 447, 448, 449, 473, 479, 490, 509, 510, 544, 561, 583, 588, 615, 632, 651, 686, 715, 726, 764

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.

Crossrefs

Cf. A035485, A035493, A035494, A035501.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    deck = []; record = 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] > record: record = deck[0]; yield n
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 11 2022

Extensions

More terms from Jud McCranie