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A181628 Numbers k such that (2^k + 3^k)/13 is prime. 2
6, 10, 14, 22, 34, 38, 82, 106, 218, 334, 4414, 7246, 10118, 10942, 15898, 42422 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified April 14 12:23 EDT 2024. Contains 371661 sequences. (Running on oeis4.)