%I A000375
%S A000375 0,1,2,4,7,10,16,22,30,38,51,65,80,101,113,139
%N A000375 Topswops (1): shuffle n cards labeled 1..n. If top card is m, reverse 
               order of top m cards. a(n) is the maximal number of steps before 
               top card is 1.
%D A000375 David Berman, M. S. Klamkin and D. E. Knuth, Problem 76-17*, A reverse 
               card shuffle, SIAM Review 19 (1977), 739-741.
%D A000375 Martin Gardner, Time Travel and Other Mathematical Bewilderments (Freeman, 
               1988), Chapter 6 [based on a column that originally appeared in Scientific 
               American, November 1974].
%D A000375 M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM 
               Review, SIAM, 1990; see p. 115-117.
%D A000375 D. E. Knuth, TAOCP, Section 7.2.1.2, Problems 107-109.
%D A000375 Andy Pepperdine, Topswops, Mathematical Gazette 73 (1989), 131-133.
%H A000375 D. E. Knuth, <a href="http://www-cs-faculty.stanford.edu/~knuth/programs.html">
               Downloadable programs</a>
%e A000375 Comment from R. K. Guy, Jan 24 2007: With 4 cards there are just two 
               perms which require 4 flips:
%e A000375 3142 --> 4132 --> 2314 --> 3214 --> 1234
%e A000375 2413 --> 4213 --> 3124 --> 2134 --> 1234
%e A000375 In these cases the deck finishes up sorted. But this is not always the 
               case - see A000376.
%Y A000375 Cf. A000376 (a variation), A123398 (number of solutions).
%Y A000375 Sequence in context: A024668 A160790 A000376 this_sequence A131752 A062365 
               A049630
%Y A000375 Adjacent sequences: A000372 A000373 A000374 this_sequence A000376 A000377 
               A000378
%K A000375 nonn,hard,nice
%O A000375 1,3
%A A000375 Bill Blewett [ billble(AT)microsoft.com ], Mike Toepke [ mtoepke(AT)microsoft.com 
               ]
%E A000375 One more term from James Kilfiger (mapdn(AT)csv.warwick.ac.uk) 7/97. 
               113 from William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Mar 
               27 2001. 139 from D. E. Knuth, Aug 25, 2001