A175521 Nonprimes k such that 9*k divides 2^(k-1) - 1.

1, 1105, 1387, 1729, 2047, 2701, 2821, 3277, 4033, 4369, 4681, 5461, 6601, 7957, 8911, 10261, 10585, 11305, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18721, 19951, 23377, 29341, 30121, 30889, 31417, 31609, 31621, 34945, 39865, 41041, 41665, 42799, 46657, 49141, 49981

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 18 2010

Keywords

• nonn

Comments

Original name was: Nonprimes n of the form 6m+1 such that (2^(n-1) mod n)=(4^(n-1) mod n)=(8^(n-1) mod n)=..=(k^(n-1) mod n) for k=2,4,8,..,smallest power of 2>n.

Examples

			1 is a term because it is a nonprime and 9*1 = 9 divides 2^(1-1) - 1 = 0.
		

Links

• Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A001567.

Cf. A000079, A091300.

Programs

Mathematica

n = 1; t = {}; While[Length[t] < 100, While[PrimeQ[n] || PowerMod[2, n-1, 9*n] != 1, n = n + 2]; AppendTo[t, n]; n = n + 2]; t (* T. D. Noe, Jul 25 2011 *)

PARI

p=0;forprime(q=2,1e5,for(n=p+1,q-1,if(Mod(2,9*n)^(n-1)==1,print1(n", ")));p=q) \\ Charles R Greathouse IV, Jul 24 2011

Extensions

Name changed by Arkadiusz Wesolowski, Jul 23 2011