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

1,1

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 Unpublished Manuscript.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

Index entries for sequences related to 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

Adjacent sequences: A213198 A213199 A213200 * A213202 A213203 A213204

Keyword

nonn,cons

Author

Joost de Winter, Mar 01 2013

Status

approved