%I #13 Mar 02 2021 02:12:32

%S 3,1,2,8,5,4,78,37,6,11,28,12,349,13,383,10,18,16,29,17,33,210,14,133,

%T 32,60,19,106,57,20,48,26,21,35,97,217,25,22,13932,863,205,54,30452,

%U 306,2591,40,44,39,49,38,51,47,30,252992198,2253,101,112,246,402,119,53,139

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

%C 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.

%D See A035490 for references, links and programs.

%o (Python)

%o def a(n):

%o deck = list(range(1, 2*maxcards+1))

%o for step in range(1, maxcards+1):

%o first, next = deck[:step], deck[step:2*step]

%o deck[0:2*step:2] = next

%o deck[1:2*step:2] = first

%o if deck[0] == n: return step

%o return '>' + str(step)

%o maxcards = 31000

%o print([a(n) for n in range(1, 54)]) # _Michael S. Branicky_, Mar 01 2021

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

%K nonn,nice

%O 1,1

%A _David W. Wilson_, Apr 22 2001