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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 \[
\lim_{n\rightarrow\infty}\frac{t_{n}}{t_{n+1}}=\lim_{n\rightarrow\infty}x_{n}=0.410098516\cdots\]
Moreover, if $u$ is the real positive number such that $1=\sum_{i=1}^{\infty}
u^{-t_i}$, then there is a positive constant $M$ such that $t_n\sim Mu^n$.

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