Finite sequences are periodic sequences. Rules are used to define these finite sequences.
A musical example is given as follows:
A song is being composed using only 2 notes (C and D). After 2 notes are played the 4th note is played based on the following rules:
If CC played then C, If DD played then C , if DC or CD played then D.
Starting with the 3 notes DCC the song will appear as the following sequence of notes:
Notice that after 7 notes the sequence repeats ad infinitum.
Note: If the second note was E instead of D in the example above the sequence above would end as Beethoven’s Fifth Symphony begins!
Given the infinite Perrin Sequence 3,0,2,3,2,5,5,7,10,12,17,22,29,… convert each number to modulo 2 which will give a series of 0’s and 1’s: