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%I #7 Oct 05 2016 10:26:26
%S 1,2,3,4,2,3,4,1,3,4,1,2,4,1,2,3,2,3,4,1,3,4,1,2,4,1,2,3,1,2,3,4,3,4,
%T 1,2,4,1,2,3,1,2,3,4,2,3,4,1,4,1,2,3,1,2,3,4,2,3,4,1,3,4,1,2,2,3,4,1,
%U 3,4,1,2,4,1,2,3,1,2,3,4,3,4,1,2,4,1,2,3,1,2,3,4,2,3,4,1,4,1,2
%N a(n) = A053839(n)+1.
%C A four-way fair share sequence. This is similar to the Thue-Morse Sequence. The Thue-Morse Sequence is the fairest way to split objects amongst two groups. If we call the groups A and B, most people split ABABABABABABABABABABABAB.......
%C This is unfair for B, because out of the best 2, A gets the best. Out of the second best 2, a gets the best. The Thue-Morse Sequence solves this:
%C ABBABAABBAABABBABAABABBAABBABAAB... The easiest way to generate the Thue-Morse Sequence is starting with a 1. Every 1 becomes 12. Every 2 becomes 21. Thus the sequence is obtained by recursion.
%C The present sequence is the same, but for splitting objects amongst 4 groups. Start with a 1. Every 1 becomes 1,2,3,4. Every 2 becomes 2,3,4,1. Every 3 becomes 3,4,1,2. Every 4 becomes 4,1,2,3.
%Y Cf. A010060, A053839.
%K nonn
%O 0,2
%A _William K. Grannis_, May 16 2016
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