A273149 a(n) = A053839(n)+1.

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, 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, 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

Offset: 0

Author

William K. Grannis, May 16 2016

Keywords

• nonn

Comments

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.......

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:

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.

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.

Crossrefs

Cf. A010060, A053839.