OEIS-Mathematica

Multipurpose Package for using OEIS On-Line data into Mathematica

This project is maintained by Psychedelic-Geometry

Mathematica OEIS Package

When you go on computing: if you are doing repetitive and boring things, is because you are not working in a proper way. So I decided to write some code to help myself with the worst part of my projects. And as this code began to grow and became more complex, thought it would be good idea to gather all together in the same Mathematica Package and to share it on the internet.

This code includes functions that can make your life easier if you a using the information from OEIS in your archives: for citation in documents or blogs, for programming sequences, or for many other purposes.

Package Description:

Version:

Changes:

Functions

Download and Install OEIS.m

https://github.com/Psychedelic-Geometry/OEIS-Mathematica/archive/master.zip

 <<OEIS`

PROGRAMMING EXAMPLES

IMPORTING DATA FROM OEIS

Importing Sequence Description

 In[1]:= OEISImport["A014321", "Description"]
 Out[1]= The next new gap between successive odd primes (divided by 2).

Importing Sequence Data:

  In[2]:= OEISImport["A080321", "Data"]
 Out[2]= {{0,0},{1,4},{2,428},{3,58747},{4,1758473969},{5,340760636747},
 {6,14410746502617904},{7,673020037180959760871},
 {8,1736622037158911219053381734718},
 {9,400539731185759177060380684246324}}

Importing Sequence creation date:

 In[3]:= OEISImport["A117321","Date"]
 Out[3]= {Mar,07,2006}

Importing Sequence Author:

 In[4]:= OEISImport["A014321", "Author"]
 Out[4]= {Hynek Mlcousek}

Importing Image:

 In[5]:= OEISImport["A030337","Image"]
 Out[5]=
[[File:Sample for A030337-Image sample.gif|border|200px]]

Importing bFile:

 In[6]:=ListPlot[OEISImport["A094358","bFile"],Joined->True]
 Out[6]= (Plot Image)

Importing Range of Available data:

 In[7]:= OEISImport["A094358","MinData"]
 Out[7]= 1
 In[8]:= OEISImport["A094358","MaxData"]
 Out[8]= 1314

EXPORTING DATA FROM OEIS:

File Extension Exported data:
*.gp Code to add help for PARI/GP functions
*.m Code to add help for Mathematica
*.txt, *.xls, *.csv, *.tsv, *.dat Data files with sequence values.
*.jpg, *.jpeg, *.jp2, *.j2k, *.bmp, *.pgn, *.gif, *.tiff, *.tif Image plot
*.bib BibTeX citation to OEIS Sequences
*.htm, *.html HTML citation to OEIS Sequences

Exporting BibTeX citation:

The input for the function can be a String or a List of Strings:

 In[1]:=OEISExport[{"A026588", "A111084"}, "example.bib"]
 Out[1]=example.bib

 @MISC{oeisA026588,
 AUTHOR={},
 TITLE={The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
 HOWPUBLISHED={\href{http://oeis.org/A026588}{A026588}},
 MONTH={},
 YEAR={},
 NOTE={Duplicate of A026572.}
 }

 @MISC{oeisA111084,
 AUTHOR={N. J. A. Sloane},
 TITLE={The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
 HOWPUBLISHED={\href{http://oeis.org/A111084}{A111084}},
 MONTH={Nov},
 YEAR={2005},
 NOTE={Where records occur in A111267.}
 }

Exporting Help Code for PARI/GP:

 In[2]:= OEISExport[{"A026588","A111084","A131473"},"code_for_PARIGP.gp"]
 Out[2]= code_for_PARIGP.gp

 addhelp(A026588,"A026588: Duplicate of A026572.");
 addhelp(A111084,"A111084: Where records occur in A111267.");
 addhelp(A131473,"A131473: a(n)=n^6-n.");

Exporting Help Code for Mathematica:

 In[3]:= OEISExport[{"A026588","A111084","A131473"},"code_for_Mathematica.m"]
 Out[3]= code_for_Mathematica.m

 A026588::usage="A026588[n]: Duplicate of A026572.";
 A111084::usage="A111084[n]: Where records occur in A111267.";
 A131473::usage="A131473[n]: a(n)=n^6-n.";

Exporting all available data

 In[4]:= OEISExport[{"A026588","A111084","A131473"},"data.xls"]
 Out[4]= {A026588_data.xls,A111084_data.xls,A131473_data.xls}

Exporting citation to HTML code

 In[5]:=OEISExport[{"A040414", "A050414", "A002323", "A026588"}, "test.html"]
 Out[5]= test.html

 <a name="oeisA040414">[1]-</a> N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences. 
 <a href=http://oeis.org/A040414">A040414</a>: Continued fraction for sqrt(435).<br/>

 <a name="oeisA050414">[2]-</a> Jud McCranie, The On-Line Encyclopedia of Integer Sequences.
 <a href=http://oeis.org/A050414">A050414</a>: Numbers n such that 2^n - 3 is prime.<br/>

 <a name="oeisA002323">[3]-</a> N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences.
 <a href=http://oeis.org/A002323">A002323</a>: Fermat remainders.<br/>

 <a name="oeisA026588">[4]-</a> The On-Line Encyclopedia of Integer Sequences.
 <a href=http://oeis.org/A026588">A026588</a>:  Duplicate of A026572.<br/>

Exporting citation to Wiki code

 In[6]:=OEISExport[{"A026518", "A111284"}, "example.wiki"]
 Out[6]:=example.wiki

 A026518: a(n) = length of n-th run of identical symbols in A026517.
 A111284: Number of permutations avoiding the patterns {2143,2341,2413,2431,3142,3241,3412,3421,4123,4213,4231,4321,4132,4312};
 number of strong sorting class based on 2143.

FUNCTIONS CREATED AUTOMATICALLY:

Function: OEISFunction[ID, Opts]:

The options Opts, are True by default, and they can be modified as:

To skip the addition of help to the function:

OEISFunction[ID,AddHelp->False]

To skip the data from the bFile:

OEISFunction[ID,bFile->False]

To do not print on the screen the information outputed:

OEISFunction[ID,Output->False]

 In[5]:= OEISFunction["A094358"]
 A094358(n): Squarefree products of factors of Fermat numbers (A023394).
 Link-1: http://oeis.org/A094358
 Link-2: http://oeis.org/b094358.txt
 Help Added: True
 Loaded data from bFile: True
 Loaded data from Sequence: False
 Data available: Table of n, A094358(n) for n=1..1314

From now on, we can use the function with all data already loaded on it:

 In[6]:= A094358[1314] 
 Out[6]= 2917004348489729

GENERATING b-Files:

Function: OEISbFile[ID,Vmax,filename]

We can define the function first, but if we do not define it, the code creates the function and preloads all available data from OEIS:

 In[5]:=A040414[0]:=20;
        A040414[n_]:=Part[{1,5,1,40},1+Mod[n-1,4}};
 In[6]:=OEISbFile["A040414", 200]
 Out[6]=b040414.txt

Links: