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, A341229, and this sequence list primes of the form (p^j + 1)/2 for j=2^0=1, j=2^1=2, ..., j=2^7=128, respectively.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..1000
EXAMPLE
(3^128 + 1)/2 = 5895092288869291585760436430706259332839105796137920554548481 = 257*275201*138424618868737*3913786281514524929*153849834853910661121, so 3 is not a term.
(113^128 + 1)/2 = 3111793506...0421698561 (a 263-digit number) is prime, so 113 is a term. Since 113 is the smallest prime p such that (p^128 + 1)/2 is prime, it is a(1) and is also A341211(7).
PROG
(PARI) isok(p) = (p>2) && isprime(p) && ispseudoprime((p^128 + 1)/2); \\ Michel Marcus, Feb 07 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 07 2021
STATUS
approved