A197943 Greatest residue of x^(n-1) (mod n), x=0..n-1.

0, 1, 1, 3, 1, 5, 1, 7, 7, 9, 1, 11, 1, 13, 10, 15, 1, 17, 1, 19, 18, 21, 1, 23, 21, 25, 25, 27, 1, 29, 1, 31, 31, 33, 30, 35, 1, 37, 36, 39, 1, 41, 1, 43, 40, 45, 1, 47, 43, 49, 49, 51, 1, 53, 49, 55, 55, 57, 1, 59, 1, 61, 58, 63, 61, 65, 1, 67, 64, 69, 1, 71, 1, 73, 69, 75, 71, 77, 1, 79, 79, 81, 1, 83, 81, 85, 82, 87, 1, 89, 78

Offset: 1

Author

Michel Lagneau, Oct 19 2011

Keywords

• nonn
• easy

Comments

a(n) = 1 if n prime and a(n) = n-1 if n even.

Examples

			a(8) = 7 because x^7 == 0, 1, 3, 5, 7  (mod 8) => 7 is the greatest residue.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11111

Crossrefs

Cf. A196082, A197929, A197930.

Programs

Mathematica

Table[Max[PowerMod[Range[0,n-1],n-1,n]], {n,100}]

PARI

A197943(n) = { my(m=0); for(x=0,n-1, m = max(m,lift(Mod(x^(n-1),n)))); (m); }; \\ Antti Karttunen, Sep 10 2018

Extensions

More terms added, incorrect PARI-program removed by Antti Karttunen, Sep 10 2018