Z. Anal. Anwend. 10(2), pp. 251-254.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: ZENTRALBLATT SUMMARY: A sequence (u_{n})_{n=1}^{∞}satisfies Benford's law if (log_{10}|u_{n}|) is uniformly distributed modulo 1. For second-order linear recurrences u_{n+2}=a_{n+2}u_{n+1}+b_{n+2}u_{n} with periodic coefficients a_{n+2}, b_{n+2} the authors prove a sufficient criterion for (u_{n}) satisfying Benford's law. As a corollary the sequences (p_{n}) and (q_{n}), where p_{n}/q_{n} denotes the n-th convergent of the continued fraction expansion of a quadratic irrational, satisfy Benford's law.
Bibtex:
@article {,
AUTHOR = {Schatte, P. AND Nagasaka, K.},
TITLE = {A note on Benford's law for second order linear recurrences with periodical coefficients},
JOURNAL = {Z. Anal. Anwend. },
YEAR = {1991},
VOLUME = {10},
NUMBER = {2},
PAGES = {251-254},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Number Theory