Abstract
Let F ( x ) be either a polynomial with real coefficients and with the leading coefficient rational or an entire function having logarithmic order α where 1 < α < 4 / 3 and taking real values at real x . Let q 1 , q 2 , … be the sequence of all the primes congruent to ℓ ( mod k ) with k > 1 a fixed integer. Let ( F ( q ) ) r denote the digits in the r -adic expansion of [ | F ( q ) | ] . We show the decimal . ( F ( q 1 ) ) r ( F ( q 2 ) ) r … , is normal to the base r .
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