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Kimberling Sequence

Given a sequence S_i as input to stage i, form sequence S_(i+1) as follows:

1. For k in [1,...,i], write term i+k and then term i-k.

2. Discard the ith term.

3. Write the remaining terms in order.

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

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.

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

See also

Out-Shuffle, Shuffle

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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."

Referenced on Wolfram|Alpha

Kimberling Sequence

Cite this as:

Weisstein, Eric W. "Kimberling Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KimberlingSequence.html

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