Combinatorica

, Volume 21, Issue 2, pp 279–291

Additive Completion of Lacunary Sequences

  • Imre Z. Ruzsa
Original Paper

DOI: 10.1007/s004930100025

Cite this article as:
Ruzsa, I. Combinatorica (2001) 21: 279. doi:10.1007/s004930100025

To the memory of Pál Erdős

Thirty years ago I read the following question of Erdőos [4]:

"Does there exist a sequence \(\) with \(\) so that every sufficiently large number is of the form \(\)? $10"

I sent my solution to Erdős in a letter (in Hungarian). He translated my letter into English and sent it to the Canadian Math. Bulletin; this became my first paper to appear.

In this paper we will find, among others, the best value of the constant c in the above question, which was also asked by Erdős.

AMS Subject Classification (2000) Classes:  11B13, 11B34, 11B83

Copyright information

© János Bolyai Mathematical Society, 2001

Authors and Affiliations

  • Imre Z. Ruzsa
    • 1
  1. 1.Alfréd Rényi Institute of Mathmatics, Hungarian Academy of Sciences; Budapest, Pf. 127, H–1364 Hungary; E-mail: ruzsa@renyi.huHU