Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.7

Solution Sequences for the Keyboard Problem and its Generalizations

Jonathan T. Rowell
University of North Carolina at Greensboro
Department of Mathematics and Statistics
116 Petty Building
317 College Avenue
Greensboro, NC 27412


The keyboard problem is an optimization problem asking how many characters can be placed into a blank document using N keystrokes. The question is representative of a larger class of output maximization problems where there is the opportunity to expand output capacity by replicating the existing output as a single unit. Here I define a generalized keyboard sequence as an integer sequence representing the maximum output of such problems, explain the construction of optimal strings of operations leading to these outputs, and demonstrate that each sequence is linearly recursive for sufficiently large N. I then evaluate two competing solutions to the keyboard problem and connect additional integer sequences to this class. The article concludes with a brief overview of the crowd-sourcing involved in the keyboard problems initial solution.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000792 A131577 A178715 A193286 A193455 A193456 A193457.)

Received June 16 2014; revised versions received March 18 2015; August 22 2015. Published in Journal of Integer Sequences, October 10 2015.

Return to Journal of Integer Sequences home page