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, A341230, A341234, A341264, and this sequence list primes of the form (p^j + 1)/2 for j=2^0=1, j=2^1=2, ..., j=2^10=1024, respectively.
EXAMPLE
(3^1024 + 1)/2 = 1866959243...6855178241 (a 489-digit number) = 59393 * 448524289 * 847036417 * 8273923970...2296603649 (a 466-digit composite number), so 3 is not a term.
(827^1024 + 1)/2 = 1677304013...0116613121 (a 2988-digit number) is prime, so 827 is a term. Since 827 is the smallest prime p such that (p^1024 + 1)/2 is prime, it is a(1) and is also A341211(10).
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 07 2021
EXTENSIONS
a(17)-a(35) from Jinyuan Wang, Feb 09 2021
STATUS
approved