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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


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

© 1996-9 Eric W. Weisstein