cp's OEIS Frontend

A080346 First card number to reach the top of the deck n times in Guy's shuffle (see A035485).

%I A080346 #38 Feb 12 2024 10:35:42
%S A080346 2,1,14,14,38,14,38,157,1,16929,170,170,170,170,170,170,170896,170896,
%T A080346 170
%N A080346 First card number to reach the top of the deck n times in Guy's shuffle (see A035485).
%C A080346 Card #1 being at the top before the first shuffle is not counted. The number of shuffles is in A080347. Card 170 reaches the top for the 15th time after 5886828 shuffles and for the 16th time after 9140809 shuffles, so a(15) and a(16) may be 170. [This was confirmed by performing 10^7 shuffles. - _Frank A. Stevenson_, Feb 04 2024]
%C A080346 Possible next term is 170896 which appears for the 20th time after 158538523553 shuffles. - _Frank A. Stevenson_, Feb 09 2024
%e A080346 Card #14 is the first card to reach the top position 3 times (after 41 shuffles) and is the first card to do so, so a(3)=14.
%o A080346 (Python) # outputs: n, A080346(n), A080347(n)
%o A080346 from collections import Counter
%o A080346 def find_terms(max_shuffles):
%o A080346   deck, times_on_top = [i for i in range(1, 2*max_shuffles+1)], Counter()
%o A080346   alst, shuffles, n = [1], 0, 1
%o A080346   while shuffles < max_shuffles:
%o A080346     shuffles += 1
%o A080346     first, next = deck[:shuffles], deck[shuffles:2*shuffles]
%o A080346     deck[0:2*shuffles:2], deck[1:2*shuffles:2] = next, first
%o A080346     times_on_top[deck[0]] += 1
%o A080346     if times_on_top[deck[0]] == n: print(n, deck[0], shuffles); n += 1
%o A080346 find_terms(35000) # _Michael S. Branicky_, Feb 01 2021
%Y A080346 Cf. A035485, A057976, A080347.
%K A080346 hard,more,nonn
%O A080346 1,1
%A A080346 _Jud McCranie_, Feb 16 2003, revised Mar 08 2003
%E A080346 Definition corrected by Lambert Klasen (vim(AT)gmx.li), Feb 08 2008
%E A080346 a(15)-a(16) confirmed by _Frank A. Stevenson_, Feb 04 2024
%E A080346 a(17)-a(19) from _Frank A. Stevenson_, Feb 09 2024