Digit functions of integer sequences. (English) Zbl 0549.10041

McLaughlin, William I.; Lundy, Sylvia A.

Fibonacci Q. 22, 105-115 (1984).

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.

Reviewer: Bodo Volkmann (Stuttgart)

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

Keywords:

Benford phenomenon; first digit problem; digit distribution; Fibonacci numbers