Katz, TM and Cohen, DIA (1986)

The first digit property for exponential sequences is independent of the underlying distribution

Fibonacci Quarterly 24(1), pp. 2-7.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

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• Zentralblatt: Zbl 0608.10054
• MathSciNet: MR0825869 (87i:11018)

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Abstract: The natural density in the set R = {cr^k: k=0,1,2, ... } where c>0, r>1 and log₁₀r is irrational, of the elements beginning with the first digit l is known to be log₁₀(1+1/l). We show that this property persists for any finitely additive, translation invariant density on sets of the form E = { cr^k + a_k: k 0,1, ... , a_k = o(r^k)}, where c>0 and log₁₀r is irrational. In particular, this includes the Fibonacci sequences.

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Bibtex:
@article {, AUTHOR = {Katz, TM and Cohen, DIA}, TITLE = {The first digit property for exponential sequences is independent of the underlying distribution}, JOURNAL = {Fibonacci Quarterly}, YEAR = {1986}, VOLUME = {24}, NUMBER = {1}, PAGES = {2-7}, }

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Reference Type: Journal Article

Subject Area(s): Number Theory

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