Formulas for the variance of digits of 1/p in base b are derived for the half-order case q=(p-1)/2, using Dedekind sums and class numbers when p≡3 mod 4 or products of Bernoulli numbers when p≡1 mod 4.
Mizuno, A certain character twisted average value of the digits of rational num- bers and the class numbers of imaginary quadratic fields, Acta Arith
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On the variance of the digits of $1/p$
Formulas for the variance of digits of 1/p in base b are derived for the half-order case q=(p-1)/2, using Dedekind sums and class numbers when p≡3 mod 4 or products of Bernoulli numbers when p≡1 mod 4.