Dense admissible sequences
Authors:
David A. Clark and Norman C. Jarvis
Journal:
Math. Comp. 70 (2001), 17131718
MSC (2000):
Primary 11B83, 11N13
Published electronically:
March 22, 2001
MathSciNet review:
1836929
Fulltext PDF Free Access
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Additional Information
Abstract: A sequence of integers in an interval of length is called admissible if for each prime there is a residue class modulo the prime which contains no elements of the sequence. The maximum number of elements in an admissible sequence in an interval of length is denoted by . Hensley and Richards showed that for large enough . We increase the known bounds on the set of satisfying and find smaller values of such that . We also find values of satisfying . This shows the incompatibility of the conjecture with the prime tuples conjecture.
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Additional Information
David A. Clark
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah, 84602
Email:
clark@math.byu.edu
Norman C. Jarvis
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah, 84602
Email:
jarvisn@math.byu.edu
DOI:
http://dx.doi.org/10.1090/S0025571801013485
PII:
S 00255718(01)013485
Received by editor(s):
August 5, 1996
Received by editor(s) in revised form:
April 18, 1997
Published electronically:
March 22, 2001
Additional Notes:
After this paper was submitted, the authors learned that Dan Gordon and Gene Rodemich have extended the calculation of $𝜌^{*}(n)$ to $n=1600$.
Article copyright:
© Copyright 2001
American Mathematical Society
