Kimberling Sequence

Given a sequence  as input to stage , form sequence  as follows:

1. For , write term  and then term .

2. Discard the th term.

3. Write the remaining terms in order.

Starting with the positive integers, the first few iterations are therefore

The diagonal elements form the sequence 1, 3, 5, 4, 10, 7, 15, ... (OEIS 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 "The On-Line Encyclopedia of Integer Sequences."