Exercise 6. Determine all sequences $\left(a_{n}\right)_{n \geqslant 1}$ of real numbers such that $a_{i}=a_{i+2020}$ for all integers $i \geqslant 1$, and such that

$$
a_{j}+2 a_{j+2} \geqslant a_{j+1}^{2}+a_{j+1}+1
$$

for all integers $\mathrm{j} \geqslant 1$.