Metric Poissonian Pair Correlation Property Part 1: The Case $n+\log n$

We prove that $(\alpha (n+\log n){)}_{n\ge 1}$ has Poissonian pair correlation for Lebesgue almost every real $\alpha$. This solves a Problem posed by Aistleitner, El-Baz and Munsch [Open Problem 2, Geom. Funct. Anal. 2021].