37 lines
1.4 KiB
Text
37 lines
1.4 KiB
Text
The [[Thue-Morse]] sequence is a sequence of ones and zeros that if two people
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take turns in the given order, the first persons turn for every '0' in the
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sequence, the second for every '1'; then this is shown to give a fairer, more
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equitable sharing of resources. (Football penalty shoot-outs for example, might
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not favour the team that goes first as much if the penalty takers take turns
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according to the Thue-Morse sequence and took 2^n penalties)
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The Thue-Morse sequence of ones-and-zeroes can be generated by:
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:''"When counting in binary, the digit sum modulo 2 is the Thue-Morse sequence"''
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;Sharing fairly between two or more:
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Use this method:
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:''When counting base '''b''', the digit sum modulo '''b''' is the Thue-Morse sequence of fairer sharing between '''b''' people.''
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;Task
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Counting from zero; using a function/method/routine to express an integer count in base '''b''',
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<br>sum the digits modulo '''b''' to produce the next member of the Thue-Morse fairshare series for '''b''' people.
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Show the first 25 terms of the fairshare sequence:
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:* For two people:
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:* For three people
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:* For five people
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:* For eleven people
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;Related tasks:
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:* [[Non-decimal radices/Convert]]
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:* [[Thue-Morse]]
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;See also:
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:* [https://oeis.org/A010060 A010060], [https://oeis.org/A053838 A053838], [https://oeis.org/A053840 A053840]: The On-Line Encyclopedia of Integer Sequences® (OEIS®)
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<br><br>
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