A268111 Integers k such that the concatenation of 2^k and 3^k is prime.

0, 1, 3, 7, 8, 21, 23, 33, 51, 88, 96, 227, 287, 1231, 1924, 3035, 3614, 4598, 6112, 10813

Offset

1,3

Comments

First five primes: 11, 23, 827, 1282187, 2566561.

a(21) > 22166. - J.W.L. (Jan) Eerland, Jul 25 2023

Links

Table of n, a(n) for n=1..20.

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

Cf. A000079, A000244.

Sequence in context: A259571 A291212 A125570 * A369920 A244532 A037208

Adjacent sequences: A268108 A268109 A268110 * A268112 A268113 A268114

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