Normality of some decimals generated by primes in a residue class

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 q1,q2,… be the sequence of all the primes congruent to ℓ(modk) 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(q1))r(F(q2))r…, is normal to the base r.