OFFSET
1,3
COMMENTS
First five primes: 11, 23, 827, 1282187, 2566561.
a(21) > 22166. - J.W.L. (Jan) Eerland, Jul 25 2023
a(21) > 55000. - Michael S. Branicky, Aug 21 2024
EXAMPLE
For k = 3 we have 2^3 and 3^3 equal to 8 and 27, respectively, and 827 is a prime number.
MATHEMATICA
Select[Range[0, 100], PrimeQ[FromDigits[Join[IntegerDigits[2^#], IntegerDigits[3^#]]]] &] (* Alonso del Arte, Jan 27 2016 *)
PROG
(PARI) isok(k) = ispseudoprime(eval(Str(2^k, 3^k))); \\ Michel Marcus, Jan 26 2016, Sep 08 2021, Jul 15 2023
(Python)
from sympy import isprime
def afind(limit, startk=0):
pow2, pow3 = 2**startk, 3**startk
for k in range(startk, limit+1):
if isprime(int(str(pow2) + str(pow3))): print(k, end=", ")
pow2 *= 2; pow3 *= 3
afind(300) # Michael S. Branicky, Sep 08 2021
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Emre APARI, Jan 26 2016
EXTENSIONS
a(12)-a(13) from Michel Marcus, Jan 26 2016
a(17)-a(19) from Michael S. Branicky, Sep 08 2021
a(20) from Michael S. Branicky, Apr 04 2023
STATUS
approved