Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.5

Generalizing the Conway-Hofstadter $10,000 Sequence

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.

(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.