A213201 Mean of leading digits in real-life sources of data, according to Benford's law (also called the first-digit law).
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
Offset: 1
Examples
3.44023696712320624882523876...
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 Unpublished Manuscript.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
- Index entries for sequences related to Benford's law
Programs
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MATLAB
digits(100);clear R;for i=1:9;R(i)=vpa([num2str(i) '*log10(1+1/' num2str(i) ')']);end;sum(R)
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MATLAB
vpa('2*log10(2)-4*log10(3)+8*log10(5)-log10(7)') -
Mathematica
RealDigits[Log[10, 1562500/567], 10, 105][[1]] (* Jean-François Alcover, Nov 28 2018 *)
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PARI
sum(d=1, 9, d*log(1+1/d)/log(10)) \\ Michel Marcus, Nov 28 2018
Formula
Equals Sum_{d=1..9} d*log(1+1/d)/log(10).