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A035493 Order in which new cards appear on top of deck in Guy's shuffling problem A035485.

%I A035493 #22 Feb 16 2025 08:32:37
%S A035493 1,2,3,6,5,9,4,16,10,12,14,23,18,20,17,27,30,33,38,37,32,11,19,53,25,
%T A035493 21,34,8,50,48,46,47,84,52,31,49,51,91,61,42,79,29,26,115,70,93,109,
%U A035493 124,97,134,111,7,129,131,157,107,123,117,96,94,72,178,86,35,121
%N A035493 Order in which new cards appear on top of deck in Guy's shuffling problem A035485.
%D A035493 D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
%D A035493 D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
%H A035493 Lars Blomberg, <a href="/A035493/b035493.txt">Table of n, a(n) for n = 1..6679</a>
%H A035493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectShuffle.html">Perfect Shuffle.</a>
%o A035493 (Python)
%o A035493 from itertools import count, islice
%o A035493 def agen(): # generator of terms
%o A035493     deck = []; tops = {1}; yield 1
%o A035493     for n in count(1):
%o A035493         deck += [2*n-1, 2*n]
%o A035493         first, next = deck[:n], deck[n:2*n]
%o A035493         deck[0:2*n:2], deck[1:2*n:2] = next, first
%o A035493         if deck[0] not in tops: tops.add(deck[0]); yield deck[0]
%o A035493 print(list(islice(agen(), 65))) # _Michael S. Branicky_, Aug 11 2022
%Y A035493 Cf. A035485, A035490, A035491, A035492, A035494, A035500.
%K A035493 nonn
%O A035493 1,2
%A A035493 _N. J. A. Sloane_, _Wouter Meeussen_
%E A035493 Extended (and corrected) by _Jud McCranie_