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Jelly (fork), 15 bytes ŒṗŒ!€ẎQ½+¥/€Æ²S Try it online! This will work for some inputs on TIO, but will fail for others due to floating point errors. However, my fork has symbolic math support, meaning that it basically never uses floats. How it works This is a brute force attempt. Times out on TIO for \$n \ge 10\$. Uses a similar approach to Kevin's answer, ...


Python 3, 72 bytes f=lambda a,n:(a[:n]in a[1:])*a[n:]or max((f(c+a,n)for c in{*a}),key=len) Try it online!


Jelly, 15 bytes ṁL*¥Œ!;`wⱮẠɗƇṗḢ Try it online! Pretty slow, uses a brute force approach with around an \$O(n \times m \times (n \times m)!)\$ complexity, where \$n\$ is the integer input and \$m\$ is the length of the string. Times out if both \$n\$ and \$m\$ are greater than 3 on TIO How it works The length of the De Bruijn sequence will always be \$m^n\$ ...


Vyxal j, 6 bytes ʁƛ:ʀƈṄ Try it Online!

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