A181628 Numbers k such that (2^k + 3^k)/13 is prime.

6, 10, 14, 22, 34, 38, 82, 106, 218, 334, 4414, 7246, 10118, 10942, 15898, 42422

Offset

1,1

Comments

All terms are of the form 2p, p prime.

The prime (2^4414 + 3^4414)/13 = 79300327387 ...611266 985181 has 2105 decimal digits.

Links

Table of n, a(n) for n=1..16.

Example

10 is in the sequence because (2^10+ 3^10)/13 = 60073/13 = 4621 is prime.

Maple

with(numtheory):for n from 1 to 4500 do: x:= (2^n + 3^n)/13:if floor(x)=x and
  type(x, prime)=true then printf(`%d, `, n):else fi:od:
# alternative
Res:= NULL:
p:= 2:
while p < 6000 do
p:= nextprime(p);
if isprime((2^(2*p)+3^(2*p))/13) then Res:= Res, 2*p fi;
od:
Res; # Robert Israel, Apr 26 2017

Prog

(PARI) is(n)=n%2==0 && isprime(n/2) && ispseudoprime((2^n+3^n)/13) \\ Charles R Greathouse IV, Jun 06 2017
(Python)
from sympy import isprime
def afind(limit, startk=1):
    k = startk
    pow2 = 2**k
    pow3 = 3**k
    for k in range(startk, limit+1):
        q, r = divmod(pow2+pow3, 13)
        if r == 0 and isprime(q):
            print(k, end=", ")
        pow2 *= 2
        pow3 *= 3
afind(1000) # Michael S. Branicky, Dec 28 2021

Crossrefs

Cf. A057469.

Sequence in context: A207574 A278972 A241817 * A023387 A315236 A315237

Adjacent sequences: A181625 A181626 A181627 * A181629 A181630 A181631

Keyword

nonn,more

Author

Michel Lagneau, Nov 18 2010

Extensions

a(12) from D. S. McNeil, Nov 18 2010

a(13) and a(14) from Robert Israel, Apr 26 2017

a(15) from Michael S. Branicky, Dec 28 2021

a(16) from Michael S. Branicky, Apr 26 2023

Status

approved