Further tabulation of the Erdös-Selfridge function

Lukes, Richard; Scheidler, Renate; Williams, Hugh

doi:10.1090/S0025-5718-97-00864-8

Further tabulation of the Erdös-Selfridge function
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by Richard F. Lukes, Renate Scheidler and Hugh C. Williams PDF

Math. Comp. 66 (1997), 1709-1717 Request permission

Abstract:

For a positive integer $k$, the Erdös-Selfridge function is the least integer $g(k) > k+1$ such that all prime factors of $\binom {g(k)}{k}$ exceed $k$. This paper describes a rapid method of tabulating $g(k)$ using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of $g(k)$. A table of values of $g(k)$ for $135 \leq k \leq 200$ is provided.

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