## Kimberling Sequence

A sequence generated by beginning with the Positive integers, then iteratively applying the following algorithm:

1. In iteration , discard the th element,

2. Alternately write the and th elements until ,

3. Write the remaining elements in order.
The first few iterations are therefore

The diagonal elements form the sequence 1, 3, 5, 4, 10, 7, 15, ... (Sloane's A007063).

References

Guy, R. K. The Kimberling Shuffle.'' §E35 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 235-236, 1994.

Kimberling, C. Problem 1615.'' Crux Math. 17, 44, 1991.

Sloane, N. J. A. Sequence A007063/M2387 in An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.