The Kimberling sequence consists of the diagonal terms of an array formed by successively applying a shuffle to a sequence. At stage , form from as follows:
1. For ,
2, ..., ,
write term
and then term
of .
2. Discard the th
term.
3. Append the terms of starting at position , in their original order.
Starting with the positive integers, the first few iterations
are therefore
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."
. At stage 
, form 
from 
as follows:
,
2, ..., 
,
write term 
and then term 
of 
.
th
term.
starting at position 
, in their original order.
![FrameBox[1] 2 3 4 5 6 7 8 9 10 11; 2 FrameBox[3] 4 5 6 7 8 9 10 11 12; 4 2 FrameBox[5] 6 7 8 9 10 11 12 13; 6 2 7 FrameBox[4] 8 9 10 11 12 13 14; 8 7 9 2 FrameBox[10] 6 11 12 13 14 15.](/images/equations/KimberlingSequence/NumberedEquation1.svg)
