login
A178491
Primes of the form 2*p^k-1, where p is prime and k > 1.
2
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
1,1
COMMENTS
Includes the Mersenne primes > 3 (A000668) and primes of the form 2p^2-1 (A092057) as subsequences. Its union with A005383 gives A178490.
LINKS
EXAMPLE
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.
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&]
PROG
(PARI) is_A178491(n) = isprime(n) & ispower((n+1)/2, , &n) & isprime(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved