Dense admissible sequences

Authors:
David A. Clark and Norman C. Jarvis

Journal:
Math. Comp. **70** (2001), 1713-1718

MSC (2000):
Primary 11B83, 11N13

DOI:
https://doi.org/10.1090/S0025-5718-01-01348-5

Published electronically:
March 22, 2001

MathSciNet review:
1836929

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-01-01348-5

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