A035492 - OEIS

%I #23 Aug 11 2022 14:48:04

%S 1,2,4,1,2,4,8,1,2,4,8,16,7,14,28,25,17,34,31,23,5,10,20,40,31,11,22,

%T 44,31,3,6,12,24,48,27,54,35,70,63,47,13,26,52,17,34,68,43,86,75,51,1,

%U 2,4,8,16,32,64,13,26,52,104,85,45,90,51

%N Position of card 1 after n-th shuffle in Guy's shuffling problem (A035485).

%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="/A035492/b035492.txt">Table of n, a(n) for n = 0..9999</a>

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

%t Transpose[Position[NestList[riguy, {}, 64], 1]][[2]] (* See A035490. *)

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     deck = []; yield 1

%o     for n in count(1):

%o         deck += [2*n-1, 2*n]

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

%o         deck[0:2*n:2], deck[1:2*n:2] = next, first

%o         yield deck.index(1) + 1

%o print(list(islice(agen(), 65))) # _Michael S. Branicky_, Aug 11 2022

%Y Cf. A035485, A035490, A035491, A035493, A035494.

%K nonn

%O 0,2

%A _Wouter Meeussen_