Summary: We investigate the integer sequence $ \left(t_{n}\right)_{n\in\mathbb{Z}}$ defined by $ t_{n}=0$ if $ n\leq0, t_{1}=1$, and $ t_{n}=\sum_{i=1}^{n-1}t_{n-t_{i}}$ for $ n \geq 2$. This sequence has the following properties: if we consider $ f_{n}(X):=-1+\sum_{i=1}^{n}X^{t_{i}}$ and take $ x_{n}$ to be the real positive number such that $ f_{n}(x_{n})=0$, then

11Y55

integer sequences