A060750 - OEIS

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

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

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