A035485 - OEIS

%I #26 Aug 15 2022 10:27:38

%S 1,2,3,1,6,5,9,1,4,2,16,10,12,14,23,16,18,20,17,27,30,33,38,10,14,37,

%T 32,6,11,19,53,37,25,21,12,34,38,8,50,48,46,14,18,23,47,53,84,52,31,

%U 49,1,51,91,61,42,79,4,29,6,49,26,23,115,4,70,93,109,11,16,19,49,18,124,97,70,10,134,111,7,38,14,79,11,129

%N Card on top of deck at n-th stage of R. K. Guy's shuffling problem.

%C At n-th step, pick up top n cards and interlace them with the next n.

%C Here is the deck after steps 0,1,2,3,4,5:

%C 1,2,3,4,5,6,7,...

%C 2,1,3,4,5,6,7,...

%C 3,2,4,1,5,6,7,...

%C 1,3,5,2,6,4,7,8,9,...

%C 6,1,4,3,7,5,8,2,9,10,...

%C It is conjectured that eventually every number appears on top of the deck.

%C See A035491 for (the relevant part of) the deck after the n-th step. - _M. F. Hasler_, Aug 13 2022

%D D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.

%D D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.

%H Lars Blomberg, <a href="/A035485/b035485.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectShuffle.html">Perfect Shuffle.</a>

%F a(n) = A035491(n,1), i.e., the first element of the n-th row of that table, for all n > 0. - _M. F. Hasler_, Aug 13 2022

%o (Python)

%o def aupton(terms):

%o   alst, deck = [1], list(range(1, 2*terms+1))

%o   for n in range(1, terms+1):

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

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

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

%o     alst.append(deck[0])

%o   return alst

%o print(aupton(83)) # _Michael S. Branicky_, Feb 01 2021

%o (PARI) A035485(n)=A035491_row(n+!n)[1]-!n \\ _M. F. Hasler_, Aug 13 2022

%Y See A035491 for the array, also A035490, A035492.

%K nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_, _Clark Kimberling_

%E More terms from _Jud McCranie_