Splinting the intriguing number 1/998001 real digits by 3, we get numbers in sequence from 000 to 999 in order...
Inspired by this curious post:https://www.linkedin.com/posts/fermatslibrary_1998001-has-all-3-digit-numbers-from-000-activity-6823588834299772928-IaRJ
The number symbolically:
In[]:=
1/998001
Out[]=
1
998001
View the digits:
In[]:=
N[1/998001]FullForm[%]Precision[%%]Accuracy[%%%]
Out[]=
1.002×
-6
10
Out[]//FullForm=
1.002003004005006`*^-6
Out[]=
MachinePrecision
Out[]=
21.9537
In[]:=
N[1/998001,200]
Out[]=
1.0020030040050060070080090100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440450460470480490500510520530540550560570580590600610620630640650660671×
-6
10
View the real digits sequence in groups of 3 numbers, discarding the first integer digit:
In[]:=
Rest[Flatten[RealDigits[N[1/998001,200]]]]
Out[]=
{0,0,2,0,0,3,0,0,4,0,0,5,0,0,6,0,0,7,0,0,8,0,0,9,0,1,0,0,1,1,0,1,2,0,1,3,0,1,4,0,1,5,0,1,6,0,1,7,0,1,8,0,1,9,0,2,0,0,2,1,0,2,2,0,2,3,0,2,4,0,2,5,0,2,6,0,2,7,0,2,8,0,2,9,0,3,0,0,3,1,0,3,2,0,3,3,0,3,4,0,3,5,0,3,6,0,3,7,0,3,8,0,3,9,0,4,0,0,4,1,0,4,2,0,4,3,0,4,4,0,4,5,0,4,6,0,4,7,0,4,8,0,4,9,0,5,0,0,5,1,0,5,2,0,5,3,0,5,4,0,5,5,0,5,6,0,5,7,0,5,8,0,5,9,0,6,0,0,6,1,0,6,2,0,6,3,0,6,4,0,6,5,0,6,6,0,6,7,0,-5}
In[]:=
Partition[Flatten[Rest[Flatten[RealDigits[N[1/998001,200]]]]],3]
Out[]=
{{0,0,2},{0,0,3},{0,0,4},{0,0,5},{0,0,6},{0,0,7},{0,0,8},{0,0,9},{0,1,0},{0,1,1},{0,1,2},{0,1,3},{0,1,4},{0,1,5},{0,1,6},{0,1,7},{0,1,8},{0,1,9},{0,2,0},{0,2,1},{0,2,2},{0,2,3},{0,2,4},{0,2,5},{0,2,6},{0,2,7},{0,2,8},{0,2,9},{0,3,0},{0,3,1},{0,3,2},{0,3,3},{0,3,4},{0,3,5},{0,3,6},{0,3,7},{0,3,8},{0,3,9},{0,4,0},{0,4,1},{0,4,2},{0,4,3},{0,4,4},{0,4,5},{0,4,6},{0,4,7},{0,4,8},{0,4,9},{0,5,0},{0,5,1},{0,5,2},{0,5,3},{0,5,4},{0,5,5},{0,5,6},{0,5,7},{0,5,8},{0,5,9},{0,6,0},{0,6,1},{0,6,2},{0,6,3},{0,6,4},{0,6,5},{0,6,6},{0,6,7}}
Again but now put it in order and in column for a better visualization:
In[]:=
Partition[Rest[Flatten[RealDigits[N[1/998001,200]]]],3]//Sort//Column
Out[]=
{0,0,2} |
{0,0,3} |
{0,0,4} |
{0,0,5} |
{0,0,6} |
{0,0,7} |
{0,0,8} |
{0,0,9} |
{0,1,0} |
{0,1,1} |
{0,1,2} |
{0,1,3} |
{0,1,4} |
{0,1,5} |
{0,1,6} |
{0,1,7} |
{0,1,8} |
{0,1,9} |
{0,2,0} |
{0,2,1} |
{0,2,2} |
{0,2,3} |
{0,2,4} |
{0,2,5} |
{0,2,6} |
{0,2,7} |
{0,2,8} |
{0,2,9} |
{0,3,0} |
{0,3,1} |
{0,3,2} |
{0,3,3} |
{0,3,4} |
{0,3,5} |
{0,3,6} |
{0,3,7} |
{0,3,8} |
{0,3,9} |
{0,4,0} |
{0,4,1} |
{0,4,2} |
{0,4,3} |
{0,4,4} |
{0,4,5} |
{0,4,6} |
{0,4,7} |
{0,4,8} |
{0,4,9} |
{0,5,0} |
{0,5,1} |
{0,5,2} |
{0,5,3} |
{0,5,4} |
{0,5,5} |
{0,5,6} |
{0,5,7} |
{0,5,8} |
{0,5,9} |
{0,6,0} |
{0,6,1} |
{0,6,2} |
{0,6,3} |
{0,6,4} |
{0,6,5} |
{0,6,6} |
{0,6,7} |
Now lets see the digits as a picture:
In[]:=
ArrayPlot[Partition[Flatten[Rest[Flatten[RealDigits[N[1/998001,200]]]]],3],Frame->None]
Out[]=
View with sorted digits as picture:
The same but in color:
Transposed and with more digits:
Listing up to 100k digits, it requires memory and some time to compute:
List dimensions:
View the fist items in the list:
View the last items in the list:
View those first items in the list as an image:
Break the digits and align them side by side to visualize:
Test the visualization with different list (matrix) size:
Convert the broken digits to integer:
Visualize the values, from the end of digits list:
Visualize the values, from the beginning of digits list:
Braking down the values to compose an image:
Braking down the values to compose an image, with the 3 digits sorted:
View the first 1000 digits as a graph:
What Wolfram|Alpha can tell us about this number 1/998001:
In[]:=
1/998001
Other interesting digit sequences to visualize, with 200 digits precision:
The digits of π is pretty random:
Notes that we didn’t change the digits for those visualizations, we just create a list of digits (an integer list so) and break the lists in matrix (list of lists) as appropriate by square root, 3, 2 or 9.
What other creative visualization we can create for the digits of 1/998001?