A262769 Integers k such that the concatenation of 2^k and k is prime.

3, 23, 63, 261, 281, 291, 4689, 10641, 11231, 12519

Offset: 1

Author

Emre APARI, Mar 24 2016

Keywords

• nonn
• base
• more

Comments

First three primes: 83, 838860823, 922337203685477580863.

a(11) > 120000. - Giovanni Resta, Apr 08 2016

a(11) > 160000. - Michael S. Branicky, Jul 06 2024

Examples

			For k = 23 we have 2^23 and 23 equal to 8388608 and 23, respectively, and 838860823 is a prime number.
		

Crossrefs

Cf. A000079.

Programs

Mathematica

Select[Range@ 5000, PrimeQ[2^# * 10^IntegerLength[#] + #] &] (* Giovanni Resta, Apr 08 2016 *)

PARI

isok(k) = isprime(eval(Str(2^k, k))); \\ Michel Marcus, Mar 23 2021

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

Extensions

a(9)-a(10) from Giovanni Resta, Apr 08 2016

a(8) inserted by Michael S. Branicky, Jul 06 2024