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The Distribution of Leading Digits and Uniform Distribution Mod 1

Persi Diaconis
The Annals of Probability
Vol. 5, No. 1 (Feb., 1977), pp. 72-81
Stable URL: http://www.jstor.org/stable/2242803
Page Count: 10
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The Distribution of Leading Digits and Uniform Distribution Mod 1
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Abstract

The lead digit behavior of a large class of arithmetic sequences is determined by using results from the theory of uniform distribution $\operatorname{mod} 1$. 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.

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