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A123250
Primes of the form 2^k + 5.
21
7, 13, 37, 2053, 140737488355333, 9007199254740997, 2787593149816327892691964784081045188247557, 11150372599265311570767859136324180752990213, 3138550867693340381917894711603833208051177722232017256453
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
Sequence in context: A201597 A158375 A144729 * A062591 A056249 A107207
KEYWORD
nonn,changed
AUTHOR
Cino Hilliard, Oct 08 2006
EXTENSIONS
a(9) from James C. McMahon, Nov 19 2024
STATUS
approved