## Digit functions of integer sequences.(English)Zbl 0549.10041

For a given sequence $$\{a_n\}$$ of natural numbers, let $$d_1(a_n),d_2(a_n),\ldots$$. denote their first, second, …digits to some base $$b$$. The authors study the joint distributions of the random variables $$d_j(x)$$ and show that, for a large class of sequences $$\{a_n\}$$, they are correlated but tend to equiprobability. They also prove that in certain cases, the non-uniform behavior of $$d_1$$ persists for all $$j$$. Thus the paper generalizes known results on “Benford behavior” $$(\text{prob}\{d_1=a\}=\log_b(1+1/a),\ a=1,\ldots,b-1)$$ in several ways.

### MSC:

 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11A63 Radix representation; digital problems