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A262769
Integers k such that the concatenation of 2^k and k is prime.
1
3, 23, 63, 261, 281, 291, 4689, 10641, 11231, 12519
OFFSET
1,1
COMMENTS
First three primes: 83, 838860823, 922337203685477580863.
a(11) > 120000. - Giovanni Resta, Apr 08 2016
a(11) > 160000. - Michael S. Branicky, Jul 06 2024
EXAMPLE
For k = 23 we have 2^23 and 23 equal to 8388608 and 23, respectively, and 838860823 is a prime number.
MATHEMATICA
Select[Range@ 5000, PrimeQ[2^# * 10^IntegerLength[#] + #] &] (* Giovanni Resta, Apr 08 2016 *)
PROG
(Python)
from sympy import isprime
def afind(limit):
k, twok = 0, 1
while k <= limit:
if isprime(int(str(twok) + str(k))): print(k, end = ", ")
k, twok = k+1, twok*2
afind(2000) # Michael S. Branicky, Mar 23 2021
(PARI) isok(k) = isprime(eval(Str(2^k, k))); \\ Michel Marcus, Mar 23 2021
CROSSREFS
Cf. A000079.
Sequence in context: A216418 A254626 A362540 * A298393 A299511 A299311
KEYWORD
nonn,base,more
AUTHOR
Emre APARI, Mar 24 2016
EXTENSIONS
a(9)-a(10) from Giovanni Resta, Apr 08 2016
a(8) inserted by Michael S. Branicky, Jul 06 2024
STATUS
approved