Acceleration of the computation of Bernoulli numbers (Q1102314)

Using an idea of Ramanujan the author constructs an interesting recurrence relation for the Bernoulli numbers \(B_ 0\), \(B_ 1\), \(B_ 2,..\). This relation yields for a fixed, but otherwise arbitrary, \(q\in\mathbb N\) a linear relation between the numbers \(B_{k-q}\), \(B_{k-3q},\ldots\). with coefficients which can be computed economically. The recurrence provides alternative ways to test whether a given prime is irregular.