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A068383 Numbers k such that k divides 11^k - 1. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A331903 A091413 A020640 * A276603 A175416 A190854

Adjacent sequences:  A068380 A068381 A068382 * A068384 A068385 A068386

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 05 2002

STATUS

approved

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Last modified July 6 04:46 EDT 2020. Contains 335475 sequences. (Running on oeis4.)