Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  111.04701
Autor:  Erdös, Pál
Title:  On a problem of Sierpinski (In English)
Source:  Atti Accad. Naz. Lincei, Rend., Cl. Sci. Fis. Mat. Nat., VIII. Ser. 23, 122-124 (1962).
Review:  Let n be a positive integer. Denote by s(k)(n) the sum of the digits of n written in the k-ary system. Let 2 = p1 < p2 < ··· be the sequence of consecutive primes. In a recent paper, Sierpinski proved that for every k limsupn = oo s(k) (pn) = oo, which immediately implies that for infinitely many n s(k) (pn+1) > s(k) (pn). The question with the opposite inequality remained open.
The author settles the question in this note by proving the Theorem: For every k there are infinitely many h for which s(k) (pn) > s(k) (pn+1). The author discusses related unsolved problems.
Reviewer:  W.E.Briggs
Classif.:  * 11A41 Elemementary prime number theory
                   11A63 Radix representation
Index Words:  number theory

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