A122095 Primes p for which 8*p+1 divides 2^p-1.

11, 29, 179, 239, 431, 761, 857, 941, 1367, 1667, 1871, 1877, 2411, 2837, 3041, 3119, 3329, 3347, 3767, 4289, 5021, 5087, 5231, 5261, 5717, 5861, 6449, 6917, 6959, 7079, 7211, 7919, 8429, 8741, 8867, 9341, 9461, 9851, 10211, 10979, 12107, 12437, 12479

Offset: 1

Author

J. Lowell, Oct 17 2006

Keywords

• nonn

Comments

The first 962 terms, all those with n<500000, are also in A023228. - R. J. Mathar, Oct 20 2006

All terms are in A023228, i.e., such that 8p+1 is prime, since a divisor of 8p+1 would also divide M(p)=A000225(p) and thus be of the form 2kp+1, but it is easily checked that 8p+1 cannot be a multiple of 2p+1 (nor of 4p+1 or 6p+1, of course). - M. F. Hasler, Mar 21 2011

Examples

			29 is in this sequence because 2^29-1 is divisible by 8 * 29 + 1 = 233.
		

Links

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

Crossrefs

Cf. A000225, A002515, A188130.

Programs

Maple

isA122095 := proc(n) RETURN( isprime(n) and ( (2^n-1) mod (8*n+1)) = 0 ) ; end: n := 1 : for a from 2 to 500000 do if isA122095(a) then print(n,a) ; n := n+1 ; fi ; od ; # R. J. Mathar, Oct 20 2006

Mathematica

Select[Prime[Range[1500]],Divisible[2^#-1,8#+1]&] (* Harvey P. Dale, Dec 18 2012 *)
Select[Prime[Range[1500]],PowerMod[2,#,8#+1]==1&] (* Harvey P. Dale, May 28 2015 *)

PARI

forprime( p=1,1e4, Mod(2,p*8+1)^p-1 || print1(p, ", "))

Extensions

More terms from R. J. Mathar, Oct 20 2006