A178490 Primes of the form 2*p^k-1, where p is prime and k >= 1.

3, 5, 7, 13, 17, 31, 37, 53, 61, 73, 97, 127, 157, 193, 241, 277, 313, 337, 397, 421, 457, 541, 577, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1249, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593

Offset: 1

Author

Farideh Firoozbakht and M. F. Hasler, Oct 09 2010

Keywords

• nonn

Comments

Includes the Mersenne primes > 3 (A000668) and primes of the form 2p^2-1 (A092057) and 2p-1 (A005383) as subsequences; excluding the latter yields A178491.

Examples

			a(1) = 7 = 2*2^2-1 and a(2) = 17 = 2*3^2-1 are also in A092057, and a(3) = 31 = 2*2^4-1 = A000668(3), but a(4) = 53 = 2*3^3-1 is in neither of these subsequences.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000668, A005383, A092057, A178491.

Programs

Maple

filter:= n -> isprime(n) and nops(numtheory:-factorset((n+1)/2))=1:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Feb 20 2024

Mathematica

Select[Prime[Range[20000]],Length[FactorInteger[(#+1)/2]]==1&]

PARI

is_A178490(n) = isprime(n) & omega((n+1)\2)==1