I have to admit, I had never seen Matula’s paper on digit sets that are “basic” in base b, very nice. And for completeness, I tracked down the “base ten with gaps example” I was vaguely remembering. It is referenced in William Gilbert’s unpublished manuscript on his website on complex based number systems. It states in base ten you can use the digits {0,1,2,3,4,50,51,52,53,54} to represent nonnegative reals, referencing Odlyzko, Non-negative digit sets in positional number systems, Proc. London Math. Soc. 37 (1978) 213-229. Alas, I don’t have access to that paper at the moment. Considering the fact that Matula’s paper came out in 1982, but was based upon a technical report dating to 1978, I wonder who should get priority for discovering digit sets that are not contiguous and still can be used to represent integers and reals. Odlyzko (first page is available) suggests a question by Knuth. And another fun result: most papers I’ve read on the topic include 0 as a digit. It turns out not to be necessary. In https://www.math.tugraz.at/fosp/pdfs/tugraz_0024.pdf they prove that in base 2 you can use the digit set {1,4} except for the leading digit, which may be {1,2,4} Steve On Dec 21, 2018, at 3:39 AM, Don Reble via math-fun <math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com>> wrote: But as balanced ternary demonstrates, that's not the only choice. Will any set of R consecutive digits do, so long as one of them is 0? For instance almost-balanced decimal, where the decimal digits are -4 through +5? Will any other set do? Other weird sets are possible. I have a vague recollection that digit sets in base ten are possible with gaps. But a search through my literature pile has been unsuccessful in tracking down the paper. Matula's paper is good. See OEIS A110081. -- Don Reble djr@nk.ca<mailto:djr@nk.ca> _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...