A178491 Primes of the form 2*p^k-1, where p is prime and k > 1.

7, 17, 31, 53, 97, 127, 241, 337, 577, 1249, 3361, 3697, 4373, 4801, 6961, 8191, 10657, 13121, 23761, 25537, 31249, 32257, 33613, 37537, 49297, 59581, 64081, 65521, 77617, 79201, 89041, 126001, 131071, 138337, 153457, 159013, 171697, 193441

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) as subsequences. Its union with A005383 gives A178490.

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, A178490.

Programs

Maple

N:= 10^6: # for terms <= N
P:= select(isprime,[2,seq(i,i=3..floor(sqrt((N+1)/2)),2)]):
R:= NULL:
for p in P do
  for k from 2 do
    v:= 2*p^k-1;
    if v > N then break fi;
    if isprime(v) then R:= R,v fi;
od od:
sort([R]); # Robert Israel, Feb 20 2024

Mathematica

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

PARI

is_A178491(n) = isprime(n) & ispower((n+1)/2,,&n) & isprime(n)