OFFSET
1,1
REFERENCES
Scott, P., and Fasli, M. (2001). Benford's law: An empirical investigation and a novel explanation. Unpublished Manuscript.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Steven Finch, Newcomb-Benford Law, August 17, 2011. [Cached copy, with permission of the author]
M. Grendar, G. Judge, L. Schechter, An empirical non-parametric likelihood family of data-based Benford-like distributions, Physica A: Statistical Mechanics and its Applications, (2007) 380, 429-438.
G. Judge and L. Schechter, Detecting problems in survey data using Benford's law, Journal of Human Resources, Winter 2009, 44, 1-24.
Zhipeng Li, Lin Cong, and Huajia Wang, Discussion on Benford's Law and its Application, arXiv:math/0408057 [math.ST], 2004.
I. Suh and T. C. Headrick, A comparative analysis of the bootstrap versus traditional statistical procedures applied to digital analysis based on Benford's Law, Journal of Forensic and Investigative Accounting, 2010, Vol. 2, No. 2, pp. 144-175.
Wikipedia, Benford's law
FORMULA
Equals Sum_{d=1..9} d*log(1+1/d)/log(10).
EXAMPLE
3.44023696712320624882523876...
MATHEMATICA
RealDigits[Log[10, 1562500/567], 10, 105][[1]] (* Jean-François Alcover, Nov 28 2018 *)
PROG
(MATLAB) digits(100); clear R; for i=1:9; R(i)=vpa([num2str(i) '*log10(1+1/' num2str(i) ')']); end; sum(R)
(MATLAB) vpa('2*log10(2)-4*log10(3)+8*log10(5)-log10(7)')
(PARI) sum(d=1, 9, d*log(1+1/d)/log(10)) \\ Michel Marcus, Nov 28 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Joost de Winter, Mar 01 2013
STATUS
approved