Algorithmic concepts for the computation of Jacobsthal's function

TL;DR

This paper reviews algorithmic approaches for computing Jacobsthal's function for primorial numbers, presents new computed values up to the 251st prime, and provides comprehensive data and sequences related to the function.

Contribution

It introduces and evaluates algorithms for Jacobsthal's function computation and supplies new data for primes up to 251, including previously unknown values.

Findings

Computed Jacobsthal's function values for primes up to 251.

Provided exhaustive lists of maximum length sequences.

Assessed practicability of different algorithmic approaches.

Abstract

The Jacobsthal function has aroused interest in various contexts in the past decades. We review several algorithmic ideas for the computation of Jacobsthal's function for primorial numbers and discuss their practicability regarding computational effort. The respective function values were computed for primes up to 251. In addition to the results including previously unknown data, we provide exhaustive lists of all sequences of the appropriate maximum lengths in ancillary files.