A068383 Numbers k such that k divides 11^k - 1.

1, 2, 4, 5, 6, 8, 10, 12, 16, 18, 20, 24, 25, 30, 32, 36, 40, 42, 48, 50, 54, 60, 64, 72, 80, 84, 90, 96, 100, 108, 114, 120, 125, 126, 128, 144, 150, 156, 160, 162, 168, 180, 192, 200, 210, 216, 222, 228, 240, 244, 250, 252, 256, 270, 272, 288, 294, 300, 312, 320

Offset: 1

Author

Benoit Cloitre, Mar 05 2002

Keywords

• easy
• nonn

Comments

For all k, 2^k, 10^k, 2 * 3^k and 10 * 3^k are in the sequence.

Examples

			11^5 - 1 = 161050, which is divisible by 5, so 5 is in the sequence.
11^6 - 1 = 1771560, which is divisible by 6, so 6 is in the sequence.
11^7 = 19487171 = 4 modulo 7, so 7 is not in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014945, A014946, A014949, A014950, A068382.

Programs

Mathematica

Join[{1}, Select[Range[500], PowerMod[11, #, #] == 1 &]] (* Robert Price, Apr 04 2020 *)

PARI

isok(n) = Mod(11, n)^n == Mod(1, n); \\ Michel Marcus, May 06 2016

Scala

def powerMod(a: Int, b: Int, m: Int): Int = b match { case 1 => a % m; case n => a * powerMod(a, n - 1, m) % m }
List(1) ++: (2 to 500).filter(k => powerMod(11, k, k) == 1) // Alonso del Arte, Apr 04 2020