A060750 Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485.

3, 1, 2, 8, 5, 4, 78, 37, 6, 11, 28, 12, 349, 13, 383, 10, 18, 16, 29, 17, 33, 210, 14, 133, 32, 60, 19, 106, 57, 20, 48, 26, 21, 35, 97, 217, 25, 22, 13932, 863, 205, 54, 30452, 306, 2591, 40, 44, 39, 49, 38, 51, 47, 30, 252992198, 2253, 101, 112, 246, 402, 119, 53, 139

Offset: 1

Author

David W. Wilson, Apr 22 2001

Keywords

• nonn
• nice

Comments

Card #1 is initially at the top of the deck and next appears at the top of the deck after 3 shuffles. Here we do not accept 0 as a valid number of shuffles and so we say that card #1 first shows up on top after 3 shuffles. A060751 and A060752 also adopt this convention. Alternatively, we can say that card #1 first shows up on top after 0 shuffles; this leads to sequences A035490, A057983, A057984, etc.

References

• See A035490 for references, links and programs.

Crossrefs

Cf. A035485, A035490, A035491, A035492, A035493, A035494, A060751, A060752.

Programs

Python

def a(n):
  deck = list(range(1, 2*maxcards+1))
  for step in range(1, maxcards+1):
    first, next = deck[:step], deck[step:2*step]
    deck[0:2*step:2] = next
    deck[1:2*step:2] = first
    if deck[0] == n: return step
  return '>' + str(step)
maxcards = 31000
print([a(n) for n in range(1, 54)]) # Michael S. Branicky, Mar 01 2021