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Generalizing the Conway-Hofstadter $10,000 Sequence
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John A. Pelesko

Department of Mathematical Sciences

University of Delaware

Newark, DE 19716

USA

**Abstract:**
We introduce a generalization of the Conway-Hofstadter $10,000 sequence. The
sequences introduced, called *k-sequences*, preserve the
Conway-Hofstadter-Fibonacci-like structure of forming terms in the sequence by
adding together two previous terms, equidistant from the start and end of the
sequence. We examine some particular *k*-sequences,
investigate relationships to
known integer sequences, establish some properties which hold for all *k*, and
show how to solve many of the defining nonlinear recursions by examining related
underlying sequences termed *clock* sequences.

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(Concerned with sequences
A004001
A004526
A004396
A037915.)

Received January 19 2004;
revised version received August 16 2004.
Published in *Journal of Integer Sequences* October 1 2004.

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