A035501 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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