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The Distribution of Leading Digits and Uniform Distribution Mod 1

Persi Diaconis
1977 Annals of Probability  
The lead digit behavior of a large class of arithmetic sequences is determined by using results from the theory of uniform distribution mod I . Theory for triangular arrays is developed and applied to binomial coefficients. A conjecture of Benford's that the distribution of digits in all places tends to be nearly uniform is verified.
doi:10.1214/aop/1176995891 fatcat:wgd7hb4igjgnzftzw2yteflc5e