shuffling

[N. J. A. Sloane]

thanks to everyone for helping extend that sequence!

this one still needs more terms please:

%I A035485
%S A035485 1,2,3,1,6,5,9,1,4,2,16,10,12
%N A035485 Card on top of deck at nth stage of Richard Guy's shuffling problem.
%O A035485 0,2


and so do these:


%I A035493
%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,
%T A035493 25,21,34,8,31,29,26,7,35,28,24,22,36,13,15
%N A035493 Order in which new cards appear on top of deck in Guy's shuffling pro
blem A035485.
%O A035493 1,2

%I A035494
%S A035494 1,2,3,6,9,16,23,27,30,33,38
%N A035494 Order in which record high new cards appear for first time on top of
deck in Guy's shuffling problem A035485.
%O A035494 1,2
 

%I A035500
%S A035500 0,1,2,4,5,6,8,10,11,12,13,14,16,17,18,19,20,21,22,25,26,28,29,
%T A035500 32,33,35,37,48,57,60,78,97,106,133,210,217,349,383}
%N A035500 Shuffles at which new cards appear on top of deck in Guy's shuffling
problem A035485.
%O A035500 1,2
%K A035500 nonn


%I A035501
%S A035501 0,1,2,4,6,10,14,19,20,21,22
%N A035501 Shuffles at which new record high cards appear on top of deck in Guy'
s shuffling problem A035485.
%O A035501 1,2


The main sequence was:

%I A035490
%S A035490 0,1,2,8,5,4,78,37,6,11,28,12,349,13,383,10,18,16,29,17,33,210,14,
%T A035490 133,32,60,19,106,57,20,48,26,21,35,97,217,25,22,13932,863,205,54,
%U A035490 30452,306,2591,40,44,39,49,38,51,47,30,252992198,2253,101,112,246,402
,119,53,139
%N A035490 Step at which card n appears on top of deck for first time in Guy's s
huffling problem A035485.
%O A035490 1,3

and thanks to several people who helped fill up three lines!


By thw ay, Richard Guy seems to say that Clark Kimberling
invented the problem, not Richard Guy.  Clark, can you confirm
this?  Of course this is different from the famous shuffling
problem you once proposed in Crux Math., but easily confused
with it.  I thought David Gale attributed this problem
to Richard, but maybe i'm mistaken.  I will copy
this directly to Richard and Clark for their comments.

NJAS