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

1,1

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.

Links

Table of n, a(n) for n=1..62.

Prog

(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

Crossrefs

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

Sequence in context: A332491 A144189 A131671 * A204025 A204126 A204113

Adjacent sequences: A060747 A060748 A060749 * A060751 A060752 A060753

Keyword

nonn,nice

Author

David W. Wilson, Apr 22 2001

Status

approved