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, A341210, A341224, and this sequence list primes of the form (p^j + 1)/2 for j=2^0=1, j=2^1=2, ..., j=2^6=64, respectively.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
EXAMPLE
(3^64 + 1)/2 = 1716841910146256242328924544641 is prime, so 3 is a term.
(5^64 + 1)/2 = 271050543121376108501863200217485427856445313 = 769*3666499598977*96132956782643741951225664001, so 5 is not a term.
MAPLE
q:= p-> (q-> q(p) and q((p^64+1)/2))(isprime):
select(q, [$3..20000])[]; # Alois P. Heinz, Feb 07 2021
MATHEMATICA
Select[Range[18000], PrimeQ[#] && PrimeQ[(#^64 + 1)/2] &] (* Amiram Eldar, Feb 07 2021 *)
PROG
(PARI) isok(p) = (p>2) && isprime(p) && ispseudoprime((p^64 + 1)/2); \\ Michel Marcus, Feb 07 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 07 2021
STATUS
approved