A196499 Numbers k such that the greatest residue of the congruence x^k (mod k) equals k-1 for x in [0..k-1].

1, 2, 3, 5, 7, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 63, 65, 67, 69, 71, 73, 74, 75, 77, 79, 81, 82, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 106, 107, 109, 111

Offset

1,2

Comments

All prime numbers are in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

50 is in the sequence because the residues  of the congruence x^50 (mod 50) are {0, 1, 24, 25, 26, 49} and the greatest value is 50 - 1 = 49.

Mathematica

lst := {}; Do[If[Max[Union[PowerMod[Range[0, n - 1], n, n]]] == n - 1, AppendTo[lst, n]], {n, 120}]; lst

Crossrefs

Cf. A196082.

Sequence in context: A195921 A175089 A047489 * A035061 A302403 A096738

Adjacent sequences: A196496 A196497 A196498 * A196500 A196501 A196502

Keyword

nonn

Author

Michel Lagneau, Oct 13 2011

Status

approved