Abstract For any positive integer k and prime p, we define an explicit set A k , p of positive integers n, having positive upper and lower density, on which the p-adic valuation of the Stirling number of the first kind s ( n + 1 , k + 1 ) is a nondecreasing function of n and is given exactly by a simple formula. This is motivated by, and extends, some recent results of Lengyel.