OFFSET
1,1
COMMENTS
A059242 is the main entry for this sequence.
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.
FORMULA
a(n) = 2^A059242(n) + 5. - Elmo R. Oliveira, Nov 08 2023
MATHEMATICA
Select[Table[2^k+5, {k, 200}], PrimeQ] (* James C. McMahon, Nov 19 2024 *)
PROG
(PARI) g(n, p) = for(k=1, n, y=p+2^k; if(isprime(y), print1(y", ")))
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Cino Hilliard, Oct 08 2006
EXTENSIONS
a(9) from James C. McMahon, Nov 19 2024
STATUS
approved