Catalan pseudoprime

In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence

${\displaystyle (-1)^{\frac {n-1}{2}}\cdot C_{\frac {n-1}{2}}\equiv 2{\pmod {n}},}$

where C_m denotes the m-th Catalan number.

The above congruence holds for every odd prime number n, so any composite n that satisfies it is pseudoprime.