Massé, B and Schneider, D (2015)

Fast growing sequences of numbers and the first digit phenomenon

International Journal of Number Theory 11:705, pp. 705--719.

ISSN/ISBN: Not available at this time. DOI: 10.1142/S1793042115500384

---

• For online information, click here.

---

Abstract: We consider a large class of fast growing sequences of numbers U_n like the nth superfactorial ∏_{1 ≤ k ≤ n} k!, the nth hyperfactorial ∏_{1 ≤ k ≤ n}k^k and similar ones. We show that their mantissas are distributed following Benford's law in the sense of the natural density. We prove that this is also verified by V_n = ∏_{1 ≤ k ≤ n} U_k, by ∏_{1 ≤ k ≤ n}V_k and is passed down to all the sequences obtained by iterating this design process. We also consider the superprimorial numbers and the products of logarithms of integers.

---

Bibtex:
@article {, AUTHOR = {Mass{\'e}, Bruno and Schneider, Dominique}, TITLE = {Fast growing sequences of numbers and the first digit phenomenon }, JOURNAL = {International Journal of Number Theory}, VOLUME = {11}, NUMBER = {705}, YEAR = {2015}, PAGES = {705--719}, DOI = {10.1142/S1793042115500384}, }

---

Reference Type: Journal Article

Subject Area(s): Analysis, Number Theory

---