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A035494 Order in which record high new cards appear for first time on top of deck in Guy's shuffling problem A035485.

%I A035494 #22 Feb 16 2025 08:32:37
%S A035494 1,2,3,6,9,16,23,27,30,33,38,53,84,91,115,124,134,157,178,222,241,267,
%T A035494 277,298,323,368,378,407,438,450,495,496,542,546,555,561,576,581,598,
%U A035494 619,646,665,703,750,774,782,806,860,862,864,905,909,937,976,1005,1052,1056,1121,1152,1197,1241,1269,1316
%N A035494 Order in which record high new cards appear for first time on top of deck in Guy's shuffling problem A035485.
%D A035494 D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
%D A035494 D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
%H A035494 Lars Blomberg, <a href="/A035494/b035494.txt">Table of n, a(n) for n = 1..3633</a>
%H A035494 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectShuffle.html">Perfect shuffle.</a>
%F A035494 Monotonic subsequence of A035493.
%o A035494 (Python)
%o A035494 from itertools import count, islice
%o A035494 def agen(): # generator of terms
%o A035494     deck = []; record = 1; yield 1
%o A035494     for n in count(1):
%o A035494         deck += [2*n-1, 2*n]
%o A035494         first, next = deck[:n], deck[n:2*n]
%o A035494         deck[0:2*n:2], deck[1:2*n:2] = next, first
%o A035494         if deck[0] > record: record = deck[0]; yield record
%o A035494 print(list(islice(agen(), 63))) # _Michael S. Branicky_, Aug 11 2022
%Y A035494 Cf. A035485, A035490, A035491, A035492, A035493, A035500, A035501.
%K A035494 nonn
%O A035494 1,2
%A A035494 _N. J. A. Sloane_, _Wouter Meeussen_
%E A035494 More terms from _Jud McCranie_