Dimensions of Copeland-Erdös Sequences

Note on Normal Decimals

It was proved by Champernowne [2] that the decimal . 1234567891011 . . . is normal, and by Besicovitch [11 that the same holds for the decimal . 1491625 . . . . Copeland and Erdös [3] have proved that if p i, P2 . . . . is any sequence of positive integers such that, for every 0 < 1, the number of p's up to n exceeds nB if n is sufficiently large, then the infinite decimal •p ip 2p 3 . . . is n...

Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem

We consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements ...

گزارش زنبورپارازیتویید (Microterys hortulanus Erdös ( Hym.: Encyrtidae از ایران

Stapled Sequences and Stapling Coverings of Natural Numbers

A stapled sequence is a set of consecutive positive integers such that no one of them is relatively prime with all of the others. The problem of existence and construction of stapled sequences of length N was extensively studied for over 60 years by Pillai, Evans, Brauer, Harborth, Erdös and others. Sivasankaranarayana, Szekeres and Pillai proved that no stapled sequences exist for any N < 17. ...

A combinatorial property and power graphs of semigroups

Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann’s theorem answering a question of Paul Erdös. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to a...