OFFSET
1,1
COMMENTS
Expressions of the form m^j + 1 can be factored (e.g., m^3 + 1 = (m + 1)*(m^2 - m + 1)) for any positive integer j except when j is a power of 2, so (p^j + 1)/2 for prime p cannot be prime unless j is a power of 2. A005383, A048161, A176116, A340480, and this sequence list primes of the form (p^j + 1)/2 for j=2^0=1, j=2^1=2, j=2^2=4, and j=2^3=8, and j=2^4=16, respectively.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
EXAMPLE
(3^16 + 1)/2 = 21523361 is prime, so 3 is a term.
(5^16 + 1)/2 = 76293945313 = 2593*29423041, so 5 is not a term.
MATHEMATICA
Select[Prime[Range[750]], PrimeQ[(#^16+1)/2]&] (* Harvey P. Dale, Oct 06 2023 *)
PROG
(PARI) isok(p) = isprime(p) && (p>2) && isprime((p^16 + 1)/2); \\ Michel Marcus, Feb 07 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 06 2021
STATUS
approved