Card 54, where are you?

[Jud McCranie]

At 05:31 AM 11/17/98 +0700, Warut Roonguthai wrote:
>I use the UBASIC code below to find how many shuffles are required for
>card n to reach the top (for the first time):
>
>10   input N
>20   clr time
>30   I=(N-1)\2
>40   while N>1
>50    inc I
>60    if N>I then N=2*(N-I)-1 else N+=N
>70   wend
>80   print I;time
>90   goto 10
>
>It took about 20 minutes on a 266-MHz Pentium II to find that card 54
>reached the top at 252992198th shuffle.  If the code was written in
>assembly language, the computation would take only a few seconds since
>each shuffle would take only a few clock cycles.  Anyone want to try?

In Pascal on a 300 MHz Pentium II, it takes about 9.6 seconds.

What is the smallest card number for which this is not known?


+-----------------------------------------------------------+
| Jud McCranie   jud.mccranie at mindspring.com or @camcat.com |
|                                                           |
| "We should regard the digital computer system as an       |
| instrument to assist the number theorist in investigating |
| the properties of his universe - the natural numbers."    |
|   -- D. H. Lehmer, 1974 (paraphrased)                     |
+-----------------------------------------------------------+