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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the smallest $k$ such that all $k\cdot 2^{n}+1$ are composite
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by G. Jaeschke PDF
Math. Comp. 40 (1983), 381-384 Request permission

Abstract:

In this note we present some computational results which restrict the least odd value of k such that $k \cdot {2^n} + 1$ is composite for all $n \geqslant 1$ to one of 91 numbers between 3061 and 78557,inclusive. Further, we give the computational results of a relaxed problem and prove for any positive integer r the existence of infinitely many odd integers k such that $k\cdot {2^r} + 1$ is prime but $k\cdot {2^v} + 1$ is not prime for $v < r$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 381-384
  • MSC: Primary 10A25; Secondary 10-04
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0679453-8
  • MathSciNet review: 679453