Distribution of Leading Digits of Numbers

The logarithmic distribution of leading digits and finitely additive measures

Distribution of the First Digits of Fibonacci Numbers

In a recent paper [1] , J. L. Brown, Jr., and R. L, Duncan showed that the sequence *{ QnFn I is uniformly distributed modulo 1 (u.d. mod 1), where c/7 denotes the natural logarithm and Fn is the/? Fibonacci number. In this paper we show that some modifications of these ideas have some interesting consequences concerning the distribution of the first digits of the Fibonacci numbers. This also a...

Perfect Numbers with Identical Digits

Suppose g ≥ 2. A natural number N is called a repdigit in base g if it has the shape a g −1 g−1 for some 1 ≤ a < g, i.e., if all of its digits in its base g expansion are equal. The number N is called perfect if σ(N) = 2N , where σ(N) := � d|N d is the usual sum of divisors function. We show that in each base g, there are at most finitely many repdigit perfect numbers, and the set of all such n...

Some Probabilistic Aspects of the Terminal Digits of Fibonacci Numbers

Notation (i) RFN (Random Fibonacci Number: An I -digit (I > 2) Fibonacci number whose subscript has been randomly chosen within the interval [Kx, K2], where Kx > 7 and K2 is much greater than Kv (ii) B(d): the probability that the initial digit of a EFN is d. (iii) E(d): the probability that the final digit of a RFN is d. (iv) (a)b: the integer a reduced modulo the integer b. (v) b \a: the inte...

Appending Digits to Generate an Infinite Sequence of Composite Numbers

Let D be a list of single digits, and let k be a positive integer. We construct an infinite sequence of positive integers by repeatedly appending, in order, one at a time, the digits from the list D to the integer k, in one of four ways: always on the left, always on the right, alternating and starting on the left, or alternating and starting on the right. In each of these four situations, we i...