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# Problem 656

## Palindromic sequences

Given an irrational number $\alpha$, let $S_\alpha(n)$ be the sequence $S_\alpha(n)=\lfloor \alpha \cdot n \rfloor - \lfloor \alpha \cdot (n-1)\rfloor$ for $n\ge 1$.
($\lfloor \ldots \rfloor$ is the floor-function.)

It can be proven that for any irrational $\alpha$ there exist infinitely many values of $n$ such that the subsequence ${S_\alpha(1),S_\alpha(2)\ldots S_\alpha(n)}$ is palindromic.