156
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A Hidden Signal in the Ulam Sequence

References

  • [Cassaigne and Finch 95] J. Cassaigne and S. Finch. “A Class of 1-additive Sequences and Quadratic Recurrences.” Exp. Math. 4: 1 (1995), 49–60.
  • [Dijkstra 82] E. Dijkstra. EWD578 More About the Function “fusc” (A Sequel to EWD570) in Selected Writings on Computing: A Personal Perspective. Springer-Verlag, 1982. pp. 230–232.
  • [Finch 91] S. Finch. “Conjectures About s-Additive Sequences.” Fibonacci Quart. 29: 3 (1991), 209–214.
  • [Finch 92] S. Finch. “Patterns in 1-Additive Sequences.” Exp. Math. 1: 1 (1992), 57–63.
  • [Finch 92] S. Finch. “On the Regularity of Certain 1-Additive Sequences.” J. Combin. Theory Ser. A 60: 1 (1992), 123–130.
  • [Ford and Zaharescu 05] K. Ford and A. Zaharescu. “On the Distribution of Imaginary Parts of Zeros of the Riemann Zeta Function.” J. Reine Angew. Math. 579 (2005), 145–158.
  • [Gibbs] P. Gibbs. “An Efficient Method for Computing Ulam Numbers.” http://vixra.org/abs/1508.0085.
  • [Guy 04] Richard K. Guy. Unsolved problems in number theory. Problem Books in Mathematics. Third edition. New York: Springer-Verlag, 2004.
  • [Lagarias 75] J. Lagarias. Problem 17, West Coast Number Theory Conferece, Asilomar,1975.
  • [Landau 11] E. Landau. “Über die Nullstellen der ζ-Funktion.” Math. Ann. 71 (1911), 548–568.
  • [Montgomery 72] H. Montgomery. “The pair correlation of zeros of the zeta function. Analytic number theory.” Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, MO, pp. 181–193,1972.
  • [Muller 66] P. Muller. M. Sc. thesis, University of Buffalo,1966.
  • [Queneau 72] R. Queneau. “Sur les suites s-additives.” J. Combin. Theory Ser. A 12 (1972), 31–71.
  • [Recaman 73] B. Recaman. “Research Problems: Questions on a Sequence of Ulam.” Am. Math. Month. 80 (1973), 919–920.
  • [Odlyzko 15] A. Odlyzko. The first 100.000 zeros of the Riemann zeta function, accurate to within 3*10− 9, downloaded 2/10/2015.
  • [The On-Line Encyclopedia of Integer Sequences 15a] “The On-Line Encyclopedia of Integer Sequences.” available from (oeis.org), 27. Nov 2015, Sequence A002858.
  • [The On-Line Encyclopedia of Integer Sequences 15b] “The On-Line Encyclopedia of Integer Sequences.” available from (oeis.org), 27. Nov 2015, Sequence A002048.
  • [The On-Line Encyclopedia of Integer Sequences 15c] “The On-Line Encyclopedia of Integer Sequences.” available from (oeis.org), 27. Nov 2015, Sequence A005242.
  • [Reznick 08] B. Reznick. “Regularity Properties of the Stern Enumeration of the Rationals.” J. Integer Seq. 11:4 (2008), Article 08.4.1, 17 pp.
  • [Roth 53] K. F. Roth. “On Certain Sets of Integers.” J. London Math. Soc. 28 (1953), 104–109.
  • [Schmerl and Spiegel 94] J. Schmerl and E. Spiegel. “The Regularity of Some 1-additive Sequences.” J. Combin. Theory Ser. A 66: 1 (1994), 172–175.
  • [Stern 55] M. Stern. “Ueber eine zahlentheoretische Funktion.” J. Reine Angew. Math. 55 (1858), 193–220.
  • [Strottman] D. Strottman. “Some Properties of Ulam Numbers.” Los Alamos Technical Report, private communication.
  • [Ulam 64] S. Ulam. “Combinatorial Analysis in Infinite Sets and Some Physical Theories.” SIAM Rev. 6 (1964) 343–355.
  • [Ulam 64] S. M. Ulam. Problems in Modern Mathematics. Science Editions. New York: John Wiley & Sons, Inc., 1964.
  • [Weyl 16] H. Weyl. “Über die Gleichverteilung von Zahlen modulo Eins.” Math. Ann. 77 (1916) 313–352.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.