Fibonacci Quarterly 24(1), pp. 2-7.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: The natural density in the set R = {cr^{k}: k=0,1,2, ... } where c>0, r>1 and log_{10}r is irrational, of the elements beginning with the first digit l is known to be log_{10}(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 log_{10}r is irrational. In particular, this includes the Fibonacci sequences.
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},
}
Reference Type: Journal Article
Subject Area(s): Number Theory