Carmichael Sequence

A Finite, Increasing Sequence of Integers $\{a_1$, ..., $a_m\}$ such that

$$(a_i-1)\vert(a_1\cdots a_{i-1})$$

for $i=1$, ..., $m$, where $m\vert n$ indicates that $m$ Divides $n$. A Carmichael sequence has exclusive Even or Odd elements. There are infinitely many Carmichael sequences for every order.

See also Giuga Sequence

References

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. ``Giuga's Conjecture on Primality.'' Amer. Math. Monthly 103, 40-50, 1996.