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:

"When counting in binary, the digit sum modulo 2 is the Thue-Morse sequence"


Sharing fairly between two or more

Use this method:

When counting base b, the digit sum modulo b is the Thue-Morse sequence of fairer sharing between b people.


Task
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:

   For two people:
   For three people
   For five people
   For eleven people


Related tasks

   Non-decimal radices/Convert
   Thue-Morse


See also

   A010060, A053838, A053840: The On-Line Encyclopedia of Integer Sequences® (OEIS®)


 
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
 
public class FairshareBetweenTwoAndMore {
 
    public static void main(String[] args) {
        for ( int base : Arrays.asList(2, 3, 5, 11) ) {
            System.out.printf("Base %d = %s%n", base, thueMorseSequence(25, base));
        }
    }
 
    private static List<Integer> thueMorseSequence(int terms, int base) {
        List<Integer> sequence = new ArrayList<Integer>();
        for ( int i = 0 ; i < terms ; i++ ) {
            int sum = 0;
            int n = i;
            while ( n > 0 ) {
                //  Compute the digit sum
                sum += n % base;
                n /= base;
            }
            //  Compute the digit sum module base.
            sequence.add(sum % base);
        }
        return sequence;
    }
 
}
 