On Rowland's sequence (Q547798)

\textit{E. S. Rowland} [J. Integer Seq. 11, No. 2, Article ID 08.2.8, 13 p., electronic only (2008; Zbl 1204.11015)] showed that the sequence \((a_k)_{k \geq 1}\) defined by \(a_1 = 7\) and \(a_k = a_{k-1} + \gcd(k, a_{k-1})\) for \(k \geq 2\), has the property that the terms of the first difference sequence \(\Delta a_k\) are either prime or 1. In this paper, the authors consider what happens when \(a_1\) is replaced by an arbitrary odd integer \(>3\). If certain technical conditions hold, they are able to show that infinitely many distinct primes occur in \(\Delta a_k\), and they also characterize these primes.