

A213201


Mean of leading digits in reallife sources of data, according to Benford's law (also called the firstdigit 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
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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 Unpublished Manuscript.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, NewcombBenford Law, August 17, 2011. [Cached copy, with permission of the author]


FORMULA

Equals Sum_{d=1..9} d*log(1+1/d)/log(10).


EXAMPLE

3.44023696712320624882523876...


MATHEMATICA



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



AUTHOR



STATUS

approved



