Problem Statement

The Thue-Morse sequence is a sequence of ones and zeros that if two people take turns in the given order, the first persons turn for every '0' in the sequence, the second for every '1'; then this is shown to give a fairer, more equitable sharing of resources. (Football penalty shoot-outs for example, might not favour the team that goes first as much if the penalty takers take turns according to the Thue-Morse sequence and took 2^n penalties) The Thue-Morse sequence of ones-and-zeroes can be generated by:

Use this method:

Counting from zero;   using a function/method/routine to express an integer count in base b, sum the digits modulo b to produce the next member of the Thue-Morse fairshare series for b people.

Show the first 25 terms of the fairshare sequence:

Let's start with the solution:

thueMorse: function [base, howmany][
    i: 0
    result: new []
    while [howmany > size result][
        'result ++ (sum digits.base:base i) % base
        i: i + 1
    ]

    return result
]

loop [2 3 5 11] 'b ->
    print [
        (pad.right "Base "++(to :string b) 7)++" =>" 
        join.with:" " map to [:string] thueMorse b 25 'x -> pad x 2
    ]