A068383 - OEIS

%I #31 Apr 25 2020 01:13:38

%S 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,

%T 84,90,96,100,108,114,120,125,126,128,144,150,156,160,162,168,180,192,

%U 200,210,216,222,228,240,244,250,252,256,270,272,288,294,300,312,320

%N Numbers k such that k divides 11^k - 1.

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

%H Seiichi Manyama, <a href="/A068383/b068383.txt">Table of n, a(n) for n = 1..10000</a>

%e 11^5 - 1 = 161050, which is divisible by 5, so 5 is in the sequence.

%e 11^6 - 1 = 1771560, which is divisible by 6, so 6 is in the sequence.

%e 11^7 = 19487171 = 4 modulo 7, so 7 is not in the sequence.

%t Join[{1}, Select[Range[500], PowerMod[11, #, #] == 1 &]] (* _Robert Price_, Apr 04 2020 *)

%o (PARI) isok(n) = Mod(11, n)^n == Mod(1, n); \\ _Michel Marcus_, May 06 2016

%o (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 }

%o List(1) ++: (2 to 500).filter(k => powerMod(11, k, k) == 1) // _Alonso del Arte_, Apr 04 2020

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

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Mar 05 2002