In[]:=
2^25
Out[]=
33554432
In[]:=
Sum[2^i,{i,25}]
Out[]=
67108862
In[]:=
%3
Out[]=
201326586
In[]:=
Sum[2^i,{i,28}]
Out[]=
536870910
In[]:=
3%
Out[]=
1610612730
{{9,{0,506}{24552,6}},​​{12,{0,3962}{253456,6}},​​{13,{0,6104}{342032,6}},​​{15,{0,27646}{20858075,0}},​​{15,{0,30074}{357007576,6}},​​

Collect winners so far....

In[]:=
Module[{sofar=2141},Reap[Monitor[Do[If[#[[2,1]]>sofar,Sow[{n,#}];sofar=#[[2,1]];]&/@result[n],{n,9,25}],n]]]
Out[]=
{Null,{{{9,{0,506}{24552,6}},{12,{0,3962}{253456,6}},{13,{0,5854}{341992,6}},{13,{0,6072}{342024,6}},{13,{0,6104}{342032,6}},{14,{0,1526}{342040,6}},{14,{0,13174}{342056,6}},{15,{0,16346}{20858069,0}},{15,{2,16365}{20858070,0}},{15,{0,27646}{20858075,0}},{15,{0,30074}{357007576,6}},{18,{2,38245}{357007584,6}},{20,{0,703870}{2586944104,6}},{20,{0,718458}{2586944112,6}},{21,{2,359229}{2586944120,6}},{21,{0,1525228}{2586944128,6}},{22,{0,2095342}{2586944152,6}},{22,{0,3929706}{2910925472,6}},{24,{0,12254886}{2910925480,6}},{24,{0,12410874}{50048859310,0}},{25,{2,6205437}{50048859312,0}},{25,{0,22401514}{50048859325,0}},{25,{0,23525994}{50048859371,0}},{25,{0,33205754}{50048862119,0}},{25,{0,33217774}{202880696061,6}}}}}
In[]:=
ToPhaseForm[{1,0,0,1,0,0,1,0,0,0,0,0}]
Out[]=
{0,{1,1,1,0}}
In[]:=
FromDigits[{1,1,1,0},2]
Out[]=
14
{4,{0,14}{419,0}},{6,{0,58}{2141,28}},
In[]:=
FromDigits[{1,1,1,0,1,0},2]
Out[]=
58
In[]:=
2^75
Out[]=
37778931862957161709568
In[]:=
N[%]
Out[]=
3.77789×
22
10
In[]:=
Length@{{4,{0,14}{419,0}},{6,{0,58}{2141,28}},{9,{0,506}{24552,6}},{12,{0,3962}{253456,6}},{13,{0,5854}{341992,6}},{15,{0,16346}{20858069,0}},{15,{0,30074}{357007576,6}},{20,{0,703870}{2586944104,6}},{22,{0,3929706}{2910925472,6}},{24,{0,12410874}{50048859310,0}},{25,{0,33217774}{202880696061,6}}}
Out[]=
11
LengthsPlotDecimal[{0,718458},20,2586944112,1000000]
{{4,{0,14}{419,0}},{6,{0,58}{2141,28}},{9,{0,506}{24552,6}},{12,{0,3962}{253456,6}},{13,{0,5854}{341992,6}},{15,{0,16346}{20858069,0}},{15,{0,30074}{357007576,6}},{20,{0,703870}{2586944104,6}},{22,{0,3929706}{2910925472,6}},{24,{0,12410874}{50048859310,0}},{25,{0,33217774}{202880696061,6}}}
In[]:=
Show[If[#[[1]]<9,LengthsPlotDecimalSmall[#[[2,1]],#[[1]],#[[2,2,1]]],LengthsPlotDecimal[#[[2,1]],#[[1]],#[[2,2,1]],8Quotient[#[[2,2,1]],8000]]],FrameTicksNone]&/@Take[{{4,{0,14}{419,0}},{6,{0,58}{2141,28}},{9,{0,506}{24552,6}},{12,{0,3962}{253456,6}},{13,{0,5854}{341992,6}},{15,{0,16346}{20858069,0}},{15,{0,30074}{357007576,6}},{20,{0,703870}{2586944104,6}},{22,{0,3929706}{2910925472,6}},{24,{0,12410874}{50048859310,0}},{25,{0,33217774}{202880696061,6}}},4]
Out[]=

,
,
,

In[]:=
Length[Last[#]]&/@TSPhaseEvolveList[{0,IntegerDigits[14,2,4]},420]
Out[]=
{4,5,5,5,5,5,6,5,6,5,6,6,6,7,7,7,8,7,8,8,8,8,8,9,9,9,10,9,10,9,10,10,10,10,10,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,14,13,14,13,14,13,14,14,14,14,14,13,14,14,14,15,15,15,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,18,17,18,17,18,17,17,17,17,17,17,17,18,17,17,17,17,17,18,18,18,19,19,19,18,18,18,17,18,18,18,18,18,17,18,18,18,18,18,19,19,19,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,18,18,18,17,18,17,18,17,17,17,17,17,17,17,17,17,18,17,17,17,16,17,17,17,18,17,17,17,16,16,16,15,16,16,16,16,16,16,16,16,16,17,17,17,16,16,16,16,16,16,16,16,16,15,16,15,16,16,16,16,16,15,15,15,15,15,15,15,14,15,15,15,16,15,16,15,15,15,14,14,14,13,13,13,14,13,14,14,14,15,15,15,14,14,14,13,14,14,14,15,15,15,15,15,16,15,15,15,14,15,15,15,15,15,16,15,15,15,15,15,16,15,15,15,16,15,15,15,15,15,16,15,15,15,15,15,16,15,16,16,16,16,16,15,16,16,16,16,16,15,16,16,16,17,17,17,17,17,16,17,17,17,17,17,16,17,17,17,17,17,18,17,17,17,16,17,17,17,16,16,16,16,16,16,16,15,16,16,16,16,16,16,16,16,16,15,15,15,15,15,14,15,15,15,15,15,14,14,14,14,14,13,13,13,12,13,13,13,12,12,12,11,12,11,11,11,10,11,11,11,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,8,8,8,8,8,7,7,7,6,6,6,6,6,5,5,5,5,5,4,4,4,3,3,3,2,2,2,1,1,1,0}
In[]:=
PuffOut[{1,1,1,1,0,1,1,1,1,0,1,0}]
In[]:=
seq=TSDirectEvolveSequence[{1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0},253456];
Out[]=
$Aborted
In[]:=
seq0=TSDirectEvolveSequence[PuffOut[IntegerDigits[506,2,9]],24552];
In[]:=
N[Count[seq0,0]/Length[seq0],3]
Out[]=
0.500
In[]:=
Count[seq0,0]/Length[seq0]
Out[]=
4093
8188
In[]:=
Table[Text@Grid[With[{u=Partition[seq0,n,1]},{Row[#],N[Count[u,#]/Length[u],4]}]&/@Tuples[{1,0},n],FrameAll],{n,4}]
Out[]=

1
0.5001
0
0.4999
,
11
0.2649
10
0.2352
01
0.2352
00
0.2646
,
111
0.09818
110
0.1667
101
0.1667
100
0.06853
011
0.1667
010
0.06853
001
0.06852
000
0.1961
,
1111
0
1110
0.09818
1101
0.1667
1100
0
1011
0.09818
1010
0.06853
1001
0.03128
1000
0.03725
0111
0.09818
0110
0.06852
0101
0
0100
0.06853
0011
0.06852
0010
0
0001
0.03724
0000
0.1589

In[]:=
1/.636
Out[]=
1.57233
In[]:=
Sqrt[GoldenRatio]//N
Out[]=
1.27202
In[]:=
PlotEvaluateTableCallout
-
2
x
2t

x
2π
3
t
,x,{x,10},{t,0,5},PlotRangeAll
General
:Exp[-4895.1] is too small to represent as a normalized machine number; precision may be lost.
General
:Exp[-19580.4] is too small to represent as a normalized machine number; precision may be lost.
General
:Exp[-44055.9] is too small to represent as a normalized machine number; precision may be lost.
General
:Further output of General::munfl will be suppressed during this calculation.
In[]:=
Off[General::munfl];PlotEvaluateTable
-
2
x
2t

x
2π
3
t
,{x,5},{t,0,100},ScalingFunctions"Log",FrameTrue,AspectRatio13

3n+1 like systems

TM emulation

Other Tag System

2007 code

Consider 2 case...

Total length = 4
Must be:

The interesting k=2 rule...

k=3

NKS rules