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

1,3

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

Table of n, a(n) for n=1..66.

Prog

(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

Crossrefs

Cf. A035485, A035493, A035494, A035501.

Sequence in context: A309882 A098380 A007782 * A024204 A036641 A260732

Adjacent sequences: A035498 A035499 A035500 * A035502 A035503 A035504

Keyword

nonn

Author

N. J. A. Sloane, Wouter Meeussen

Extensions

More terms from Jud McCranie

Status

approved