Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 747.11006
Autor: Erdös, Paul; Joó, I.
Title: On the expansion 1 = sum q-ni. (In English)
Source: Period. Math. Hung. 23, No.1, 25-28 (1991); Corrigendum ibid. 25, No.1, 113 (1992)
Review: The authors consider the q-adic expansions 1 = sumoon = 1\epsilonn/qn, \epsilonn = 0 or 1, where 1 < q < 2. They consider the digits in the greedy and lazy expansions above and show in the case of the greedy expansion: (a) For fixed q there are no arbitrarily long sequences of consecutive 1 digits in the sequence \epsilon1(1), \epsilon2(1),.... (b) The set of 1 < q < 2 for which the greedy expansion contains arbitrarily long 0- sequences is residual in (1,2) and has measure 1.
By contrast for the lazy expansion they show that the set of 1 < q < 2 for which the lazy expansion contains arbitrarily long 1-sequences is residual and of full measure in (1,2).
The text of the Corrigendun should be added to theorem 2.
Reviewer: A.Knopfmacher (Wits)
Classif.: * 11A67 Representation systems for integers and rationals
11A63 Radix representation
Keywords: digits; lazy expansions; greedy expansion
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