### Deligny, H and Jolissaint, P (2013)

#### Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]

Elemente der Mathematik, 68(1), pp. 9-21.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.4171/EM/213

Note - this is a foreign language paper: FRE

**Abstract:** A sequence of positive numbers (a_n) satisfies Benford's Law if, for every digit d between 1 and 9, the proportion of values of the indices n for which a_n has d as first digit is equal to log_{10}(1+1/d). In two previous articles, the second co-author studied sequences (a_n) that satisfy linear recurrence equations of the form
a_{n+k}=c_{k-1}a_{n+k-1}+c_{k-2}a_{n+k-2}+\ldots+c_1a_{n+1}+c_0a_n,
and he provided sufficient conditions on the roots of the characteristic polynomial
p(x)=x^k-c_{k-1}x^{k-1}-\ldots-c_1x-c_0
of the relation that ensure that (a_n) satisfies Benford's Law. Here, we give sufficient conditions directly on the coefficients c_0,...,c_{k-1} in order that solutions of such recurrence relations satisfy the same law. Emphasis is put on many cases where the coefficients are non negative real numbers.

**Bibtex:**

```
@article {,
AUTHOR = {Hugues Deligny and Paul Jolissaint},
TITLE = {Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]},
JOURNAL = {Elemente der Mathematik},
YEAR = {2013},
VOLUME = {68},
NUMBER = {1},
PAGES = {9--21},
DOI = {10.4171/EM/213},
URL = {http://www.ems-ph.org/journals/show_abstract.php?issn=0013-6018&vol=68&iss=1&rank=2},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Analysis, Dynamical Systems