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®)


fcn fairShare(n,b){    // b<=36
   n.pump(List,'wrap(n){ n.toString(b).split("").apply("toInt",b).sum(0)%b })
}
foreach b in (T(2,3,5,11)){
   println("%2d: %s".fmt(b,fairShare(25,b).pump(String,"%2d ".fmt)));
}