Suggested and reformulated from the internet by Terrell L. Hill.
Using Maple (first!, please no cheating) find the beginning of the infinite sequence of the problem below, find the locations of the 0's and make a conjecture.
If you want, prove your conjecture by human means.
Problem: (Generalized and recast in my vocabulary) We have an
infinite linear array of points numbered 1,2,3,4,... Each point can be
either in state 0 or state 1. At the outset, each point is in state 1.
Step 1: Beginning with point 1, change the state of each point (i.e.,
from 1 to 0).
Step 2: Beginning with point 2, change the state of every second point
(2,4,6,...).
Step 3: Beginning with point 3, change the state of every third point
(3,6,9,...).
Etc.
Step n: Beginning with point n, change the state of every n-th point
(n,2n,3n,...).
Etc.
What is the final configuration of states?