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A268111 Integers k such that the concatenation of 2^k and 3^k is prime. 0

%I

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

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

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

%e For k = 3 we have 2^3 and 3^3 equal to 8 and 27, respectively, and 827 is a prime number.

%t Select[Range[0,100], PrimeQ[FromDigits[Join[IntegerDigits[2^#], IntegerDigits[3^#]]]] &] (* _Alonso del Arte_, Jan 27 2016 *)

%o (PARI) isok(n) = isok(n) = isprime(eval(Str(2^n, 3^n))); \\ _Michel Marcus_, Jan 26 2016 and Sep 08 2021

%o (Python)

%o from sympy import isprime

%o def afind(limit, startk=0):

%o pow2, pow3 = 2**startk, 3**startk

%o for k in range(startk, limit+1):

%o if isprime(int(str(pow2) + str(pow3))): print(k, end=", ")

%o pow2 *= 2; pow3 *= 3

%o afind(300) # _Michael S. Branicky_, Sep 08 2021

%Y Cf. A000079, A000244.

%K nonn,base,more

%O 1,3

%A _Emre APARI_, Jan 26 2016

%E a(12)-a(13) from _Michel Marcus_, Jan 26 2016

%E a(17)-a(19) from _Michael S. Branicky_, Sep 08 2021

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)