A080346 First card number to reach the top of the deck n times in Guy's shuffle (see A035485).

2, 1, 14, 14, 38, 14, 38, 157, 1, 16929, 170, 170, 170, 170, 170, 170, 170896, 170896, 170

Offset

1,1

Comments

Card #1 being at the top before the first shuffle is not counted. The number of shuffles is in A080347. Card 170 reaches the top for the 15th time after 5886828 shuffles and for the 16th time after 9140809 shuffles, so a(15) and a(16) may be 170. [This was confirmed by performing 10^7 shuffles. - Frank A. Stevenson, Feb 04 2024]

Possible next term is 170896 which appears for the 20th time after 158538523553 shuffles. - Frank A. Stevenson, Feb 09 2024

Links

Table of n, a(n) for n=1..19.

Example

Card #14 is the first card to reach the top position 3 times (after 41 shuffles) and is the first card to do so, so a(3)=14.

Prog

(Python) # outputs: n, A080346(n), A080347(n)
from collections import Counter
def find_terms(max_shuffles):
  deck, times_on_top = [i for i in range(1, 2*max_shuffles+1)], Counter()
  alst, shuffles, n = [1], 0, 1
  while shuffles < max_shuffles:
    shuffles += 1
    first, next = deck[:shuffles], deck[shuffles:2*shuffles]
    deck[0:2*shuffles:2], deck[1:2*shuffles:2] = next, first
    times_on_top[deck[0]] += 1
    if times_on_top[deck[0]] == n: print(n, deck[0], shuffles); n += 1
find_terms(35000) # Michael S. Branicky, Feb 01 2021

Crossrefs

Cf. A035485, A057976, A080347.

Sequence in context: A063613 A245733 A276851 * A216445 A124026 A106204

Adjacent sequences: A080343 A080344 A080345 * A080347 A080348 A080349

Keyword

hard,more,nonn

Author

Jud McCranie, Feb 16 2003, revised Mar 08 2003

Extensions

Definition corrected by Lambert Klasen (vim(AT)gmx.li), Feb 08 2008

a(15)-a(16) confirmed by Frank A. Stevenson, Feb 04 2024

a(17)-a(19) from Frank A. Stevenson, Feb 09 2024

Status

approved