Resumen de Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire

Jean Paul Bézivin

• Let $a,b$ be coprime rational integers, and $u(n)$ the binary recurrent sequence $u(n+2)=au(n+1)+bu(n)$, with the initial values $u(0)=0$ and $u(1)=1$. It is proved in [4] that the quotient of the logarithm of the product of the $u(k), 1\leq k\leq n$, and of the logarithm of the least common multiple of the $ u(k), 1\leq k\leq n$, converges to $\pi^2/6$ when $n$ goes to infinity. In this paper, we generalize this result to other recurrent sequences. As an example, fot the binary sequence above with initial values $u(0)=2$ and $u(1)=a$, the limit is $\pi^2/8$.