OFFSET
1,1
COMMENTS
Composite n are Fermat weak pseudoprimes to base a(n).
If n > 2 is prime then a(n) = 2. The converse is false : a(341) = 2 and 341 isn't prime.
For n > 1, a(n) <= n and if a(n) = n, then A105222(n) = n+1.
It seems that a(n) = n if and only if n = 2^k with k > 0, a(n) = n-1 if and only if n = 3^k with k > 0, a(2n) = n if and only if n = p^k where p is an odd prime and k > 0. - Thomas Ordowski, Oct 19 2017
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
GĂ©rard P. Michon, Weak pseudoprimes to base a
EXAMPLE
We have 2^4 != 2, 3^4 != 3, but 4^4 == 4 (mod 4), so a(4) = 4.
MAPLE
L:=NULL:for n to 100 do for a from 2 while a^n - a mod n !=0 do od; L:=L, a od: L;
MATHEMATICA
a[n_] := Block[{m = 2}, While[PowerMod[m, n, n] != Mod[m, n], m++]; m]; Array[a, 100] (* Giovanni Resta, Mar 19 2014 *)
PROG
(Haskell)
import Math.NumberTheory.Moduli (powerMod)
a239452 n = head [m | m <- [2..], powerMod m n n == mod m n]
-- Reinhard Zumkeller, Mar 19 2014
(Python)
L=[];
for n in range(1, 101):
...a=2
...while (a**n - a) % n != 0:
......a+=1
...L=L+[a]
L
(PARI) a(n)=my(m=2); while(Mod(m, n)^n!=m, m++); m \\ Charles R Greathouse IV, Mar 21 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert FERREOL, Mar 19 2014
EXTENSIONS
a(20)-a(77) from Giovanni Resta, Mar 19 2014
STATUS
approved