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Massť, 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



Abstract: We consider a large class of fast growing sequences of numbers Un like the nth superfactorial ∏1 ≤ k ≤ n k!, the nth hyperfactorial ∏1 ≤ k ≤ nkk 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 Vn = ∏1 ≤ k ≤ n Uk, by ∏1 ≤ k ≤ nVk 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