Fibonacci Quarterly 7(5), pp. 474-475.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: The initial digit problem is concerned with the distribution of the first digits which occur in the set of all positive integers. If A is the set of all positive integers with initial digit a, then the asymptotic density of A, if it exists, would provide a suitable answer to the question "What is the probability that an integer chosen at random has initial digit equal to a?". However, it is easily shown that the asymptotic density doesn't exist. The purpose of this note is to show that the logarithmic density of A exists and is equal to log (1+1/a), where log x is the common logarithm.
Bibtex:
@article {,
AUTHOR = {Duncan, R. L.},
TITLE = {Note on the initial digit problem},
JOURNAL = {Fibonacci Quarterly},
YEAR = {1969},
VOLUME = {7},
NUMBER = {5}
PAGES = {474--475},
URL = {http://www.fq.math.ca/Scanned/7-5/duncan.pdf},
}
Reference Type: Journal Article
Subject Area(s): Number Theory