A123250 Primes of the form 2^k + 5.

7, 13, 37, 2053, 140737488355333, 9007199254740997, 2787593149816327892691964784081045188247557, 11150372599265311570767859136324180752990213

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.

Links

Table of n, a(n) for n=1..8.

Formula

a(n) = 2^A059242(n) + 5. - Elmo R. Oliveira, Nov 08 2023

Prog

(PARI) g(n, p) = for(k=1, n, y=p+2^k; if(isprime(y), print1(y", ")))

Crossrefs

Cf. A000040, A059242.

Sequence in context: A201597 A158375 A144729 * A062591 A056249 A107207

Adjacent sequences: A123247 A123248 A123249 * A123251 A123252 A123253

Keyword

nonn

Author

Cino Hilliard, Oct 08 2006

Status

approved