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 A123250 #13 Nov 19 2024 22:14:32
%S A123250 7,13,37,2053,140737488355333,9007199254740997,
%T A123250 2787593149816327892691964784081045188247557,
%U A123250 11150372599265311570767859136324180752990213,3138550867693340381917894711603833208051177722232017256453
%N A123250 Primes of the form 2^k + 5.
%C A123250 A059242 is the main entry for this sequence.
%C A123250 If 2^n + 5 is prime then n is odd. Proof: Lemma 1: a^n+b^n = (a+b)(a^n-1 - a^(n-2)b + ... + b^(n-1)) 2^n + 5 = 2*(2^(n-1)+1) + 3. Then if n is even, n-1 is odd and by Lemma 1, 2+1 divides 2*(2^(n-1)+1) and thus divides 2^n+5 so it cannot be prime.
%F A123250 a(n) = 2^A059242(n) + 5. - _Elmo R. Oliveira_, Nov 08 2023
%t A123250 Select[Table[2^k+5,{k,200}],PrimeQ] (* _James C. McMahon_, Nov 19 2024 *)
%o A123250 (PARI) g(n,p) = for(k=1,n,y=p+2^k;if(isprime(y),print1(y",")))
%Y A123250 Cf. A000040, A059242.
%K A123250 nonn
%O A123250 1,1
%A A123250 _Cino Hilliard_, Oct 08 2006
%E A123250 a(9) from _James C. McMahon_, Nov 19 2024