A035494 Order in which record high new cards appear for first time on top of deck in Guy's shuffling problem A035485.

1, 2, 3, 6, 9, 16, 23, 27, 30, 33, 38, 53, 84, 91, 115, 124, 134, 157, 178, 222, 241, 267, 277, 298, 323, 368, 378, 407, 438, 450, 495, 496, 542, 546, 555, 561, 576, 581, 598, 619, 646, 665, 703, 750, 774, 782, 806, 860, 862, 864, 905, 909, 937, 976, 1005, 1052, 1056, 1121, 1152, 1197, 1241, 1269, 1316

Offset

1,2

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..3633

Eric Weisstein's World of Mathematics, Perfect shuffle.

Formula

Monotonic subsequence of A035493.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    deck = []; record = 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] > record: record = deck[0]; yield record
print(list(islice(agen(), 63))) # Michael S. Branicky, Aug 11 2022

Crossrefs

Cf. A035485, A035490, A035491, A035492, A035493, A035500, A035501.

Sequence in context: A026735 A006868 A067435 * A003244 A115995 A051057

Adjacent sequences: A035491 A035492 A035493 * A035495 A035496 A035497

Keyword

nonn

Author

N. J. A. Sloane, Wouter Meeussen

Extensions

More terms from Jud McCranie

Status

approved