A035500 -id:A035500 - cp's OEIS frontend

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

N. J. A. Sloane, Wouter Meeussen

nonn

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.

Lars Blomberg, Table of n, a(n) for n = 1..3633
Eric Weisstein's World of Mathematics, Perfect shuffle.

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

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

Monotonic subsequence of A035493.

More terms from Jud McCranie

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

Original entry on oeis.org

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

N. J. A. Sloane, Wouter Meeussen

nonn

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.

Lars Blomberg, Table of n, a(n) for n = 1..6679
Eric Weisstein's World of Mathematics, Perfect Shuffle.

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

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

Extended (and corrected) by Jud McCranie

cp's OEIS Frontend

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

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