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A213201 Mean of leading digits in real-life sources of data, according to Benford's law (also called the first-digit law). 4
3, 4, 4, 0, 2, 3, 6, 9, 6, 7, 1, 2, 3, 2, 0, 6, 2, 4, 8, 8, 2, 5, 2, 3, 8, 7, 6, 0, 0, 3, 9, 9, 4, 4, 4, 0, 9, 1, 0, 6, 7, 7, 2, 8, 5, 8, 1, 4, 0, 5, 9, 9, 8, 8, 6, 3, 1, 4, 3, 3, 7, 7, 1, 8, 2, 9, 8, 1, 8, 0, 8, 1, 3, 3, 1, 6, 7, 2, 9, 2, 8, 4, 8, 4, 0, 4, 5, 1, 5, 3, 6, 8, 5, 2, 9, 2, 9, 1, 8, 8, 3, 7, 2, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
Scott, P., and Fasli, M. (2001). Benford's law: An empirical investigation and a novel explanation. Unpublished Manuscript.
LINKS
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
Sequence in context: A038018 A108658 A240669 * A245843 A188729 A222509
KEYWORD
nonn,cons
AUTHOR
Joost de Winter, Mar 01 2013
STATUS
approved

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Last modified April 12 19:05 EDT 2024. Contains 371636 sequences. (Running on oeis4.)