Table of Contents
International Journal of Combinatorics
Volume 2014 (2014), Article ID 214637, 8 pages
http://dx.doi.org/10.1155/2014/214637
Research Article

Midpoint-Free Subsets of the Real Numbers

School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

Received 22 May 2014; Accepted 29 July 2014; Published 26 August 2014

Academic Editor: Chris A. Rodger

Copyright © 2014 Roger B. Eggleton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Sloane, OEIS—Online Encyclopedia of Integer Sequences, Note A003002 and A005836 in particular; many relevant links are included.
  2. R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, NY, USA, 3rd edition, 2004.
  3. J. Dybizbański, “Sequences containing no 3-term arithmetic progressions,” Electronic Journal of Combinatorics, vol. 19, no. 2, pp. 1–15, 2012. View at Google Scholar · View at MathSciNet
  4. D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin, London, UK, 1986.
  5. S. Yates, “Prime divisors of repunits,” Journal of Recreational Mathematics, vol. 8, no. 1, pp. 33–38, 1975. View at Google Scholar · View at MathSciNet
  6. J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman, and S. Wagstaff Jr., “Factorizations of bn±1,b=2,3,5,6,7,10,11,12 up to high powers,” Contemporary Mathematics, vol. 22, 1983. View at Google Scholar
  7. P. Erdős and P. Turán, “On some sequences of integers,” Journal of the London Mathematical Society, vol. 28, pp. 104–109, 1936. View at Google Scholar