Look-and-say sequence: Difference between revisions

Line 2,910:

=={{header|Mathematica}}/{{header|Wolfram Language}}==

Custom Functions:

<lang Mathematica>~~RunLengthEncode~~[~~x_List~~]:=~~(Through~~[~~{First~~,~~Length}[#]]&)~~/@Split[x]

<lang Mathematica> LookAndSay[n_Integer?Positive]:=Map[Reverse,Tally/@Split@IntegerDigits@n,2]//Flatten//FromDigits</lang>

LookAndSay[n_,d_:1]:=NestList[Flatten[Reverse/@RunLengthEncode[#]]&,{d},n-1]</lang>

This function, which works for arbitrary positive integers, starts with `n` and generates the next member of the sequence.

If second argument is omitted the sequence is started with 1. Second argument is supposed to be a digits from 0 to 9. If however a larger number is supplied it will be seen as 1 number, not multiple digits. However if one wants to start with a 2 or more digit number, one could reverse the sequence to go back to a single digit start. First example will create the first 13 numbers of the sequence starting with 1, the next example starts with 7:

The first example returns the first 13 numbers of the sequence starting with 1. Entering

⚫

<lang Mathematica>~~FromDigits~~ /@ ~~LookAndSay[13~~] // Column

FromDigits /@ LookAndSay[13, 7] // Column</lang>

⚫

<lang Mathematica>NestList[LookAndSay, 1, 12] // Column</lang>

gives back:

returns

<pre style='height:15em;overflow:scroll'>1

Line 2,934:

1321132132111213122112311311222113111221131221

Entering 7:

7

<lang Mathematica>NestList[LookAndSay, 7, 12] // Column</lang>

generates:

<pre style='height:15em;overflow:scroll'>7

17

1117