OFFSET
1,1
COMMENTS
Composite n are Fermat pseudoprimes to base a(n).
For n > 1; (5+(-1)^n)/2 <= a(n) <= n+(-1)^n. If n > 2 and a(n) > 2 then n is composite. - Thomas Ordowski, Dec 01 2013
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Wikipedia, Fermat pseudoprime
FORMULA
a(p) = 2 for odd prime p.
EXAMPLE
We have 2^(2-1) == 0, 3^(2-1) == 1 (mod 2), so a(2) = 3.
MATHEMATICA
Table[k = 2; While[PowerMod[k, n - 1, n] != 1, k++]; k, {n, 2, 100}] (* T. D. Noe, Dec 07 2013 *)
PROG
(PARI) a(n) = {m = 2; while ((m^(n-1) % n) != lift(Mod(1, n)), m++); m; } \\ Michel Marcus, Dec 01 2013
(PARI) a(n) = my(m=2); while(Mod(m, n)^(n-1)!=1, m++); m \\ Charles R Greathouse IV, Dec 01 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Max Alekseyev, Apr 14 2005
STATUS
approved