shuffling news

[N. J. A. Sloane]

Wouter, thanks very much!
Based on what you and Colin sent i have added the following
sequences.  Of course there's much more to be done!
Neil

%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
%N A035490 Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485.
%O A035490 1,3
%K A035490 nonn
%Y A035490 Cf. A035485, A035491-A035494.
%A A035490 Wouter Meeussen (eu000949 at pophost.eunet.be)
%t A035490 riguy[deck_List]:= Module[{le=Length[deck]}, Flatten[Transpose[ Reverse@ Partition[Flatten[{deck,le+1,le+2 }],le/2+1] ]]]
%t A035490 Table[Length[FixedPoint[riguy,{},SameTest->(#2[[1]]=== i &)]]/2,{i,2,38}]
%E A035490 a(39)=13932 supplied by Colin Mallows (clm at research.att.com)

%I A035491
%S A035491 2,1,3,2,4,1,1,3,5,2,6,4,6,1,4,3,7,5,8,2,5,6,8,1,2,4,9,3,10,7,
%T A035491 9,5,3,6,10,8,7,1,11,2,12,4,1,9,11,5,2,3,12,6,4,10,13,8,14,7,
%U A035491 4,1,10,9,13,11,8,5,14,2,7,3,15,12,16,6,2,4,7,1,3,10,15,9,12,13,16,11,6,8,17,5,18,14,
%N A035491 Relevant part of deck in Guy's shuffling problem (A035485) regarded as a triangular array.
%O A035491 1,1
%K A035491 nonn,tabl
%A A035491 Wouter Meeussen (eu000949 at pophost.eunet.be)
%e A035491 {}, {2, 1}, {3, 2, 4, 1}, {1, 3, 5, 2, 6, 4}, {6, 1, 4, 3, 7, 5, 8, 2},...
%t A035491 NestList[riguy,{},12]//ColumnForm // See A035490.
%Y A035491 Cf. A035485, A035490-A035494.

%I A035492
%S A035492 1,2,4,1,2,4,8,1,2,4,8,16,7,14,28,25,17,34,31,23,5,10,20,40,31,11,22,44,31,3,6,
%T A035492 12,24,48,27,54,35,70,63,47,13,26,52,17,34,68,43,86,75,51,1,2,4,8,16,32,64,
%U A035492 13,26,52,104,85,45,90,51
%N A035492 Position of card 1 after nth shuffle in Guy's shuffling problem (A035485).
%O A035492 1,2
%K A035492 nonn
%A A035492 Wouter Meeussen (eu000949 at pophost.eunet.be)
%t A035492 Position[NestList[riguy,{},64],1]; Transpose[%][[2]] // See See A035490.
%Y A035492 Cf. A035485, A035490-A035494.

%I A035493
%S A035493 1,2,3,6,5,9,4,16,10,12
%N A035493 Order in which new cards appear for first time on top of deck in Guy's shuffling problem A035485.
%O A035493 1,2
%K A035493 nonn
%Y A035493 Cf. A035485, A035490-A035492, A035494.
%A A035493 njas, Wouter Meeussen (eu000949 at pophost.eunet.be)

%I A035494
%S A035494 1,2,3,6,9,16
%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
%K A035494 nonn
%Y A035494 Cf. A035485, A035490-A035493.
%F A035494 Monotonic subsequence of A035493.
%A A035494 njas, Wouter Meeussen (eu000949 at pophost.eunet.be)