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math.NT2013★ 2 cited
A short note on Jacobsthal's function
Fintan Costello, Paul Watts
The function g(n) represents the smallest number Q such that every sequence of Q consecutive integers contains an integer coprime to n. We give a new and explicit upper bound on th…
math.NT2012
Jacobsthal's function and a generalisation of Euler's totient
Fintan Costello, Paul Watts
Jacobsthal's function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to P_k, the product of the first k primes…
math.NT2012★ 2 cited
A computational upper bound on Jacobsthal's function
Fintan Costello, Paul Watts
The function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to the first k primes. We give a new computational…