Summary
We compute a formula for the statistical average of numbers whose base two expression has no more than a given number of digits and contains a given number of ones. We call the collection of such numbers a Hamming circle centered at 0 and conjecture a formula for the mean of Hamming circles centers at any positive integer.
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Disclosure statement
No potential conflict of interest was reported by the author(s).
Acknowledgment
The author would like to thank the referees for their comments and suggestions.
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Chris Boucher
CHRIS BOUCHER (MR Author ID: 646099) received his Ph.D. from the University of Massachusetts in 1998. He is currently a professor in and interim chair of the Mathematics Department at Salem State University in Salem, MA. His primary research interests are probability and mathematical computing, but he considers himself a mathematical omnivore. His outside interests include basketball, spending time with his wife and two children, and overly ambitious home renovation projects.