This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341210 #14 Oct 06 2023 13:41:19 %S A341210 3,29,41,73,113,157,167,173,199,599,607,617,1213,1747,1979,2027,2237, %T A341210 2377,2441,2593,2659,2689,2693,3061,3137,3413,3457,3539,3673,3733, %U A341210 3769,4091,4157,4273,4289,4547,4603,4759,4877,4909,4957,5039,5231,5233,5303,5419 %N A341210 Primes p such that (p^16 + 1)/2 is prime. %C A341210 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. %H A341210 Jon E. Schoenfield, <a href="/A341210/b341210.txt">Table of n, a(n) for n = 1..10000</a> %e A341210 (3^16 + 1)/2 = 21523361 is prime, so 3 is a term. %e A341210 (5^16 + 1)/2 = 76293945313 = 2593*29423041, so 5 is not a term. %t A341210 Select[Prime[Range[750]],PrimeQ[(#^16+1)/2]&] (* _Harvey P. Dale_, Oct 06 2023 *) %o A341210 (PARI) isok(p) = isprime(p) && (p>2) && isprime((p^16 + 1)/2); \\ _Michel Marcus_, Feb 07 2021 %Y A341210 Primes p such that (p^(2^k) + 1)/2 is prime: A005383 (k=0), A048161 (k=1), A176116 (k=2), A340480 (k=3), (this sequence) (k=4). %K A341210 nonn %O A341210 1,1 %A A341210 _Jon E. Schoenfield_, Feb 06 2021