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%I #43 Jul 25 2023 09:13:47
%S 0,1,3,7,8,21,23,33,51,88,96,227,287,1231,1924,3035,3614,4598,6112,
%T 10813
%N Integers k such that the concatenation of 2^k and 3^k is prime.
%C First five primes: 11, 23, 827, 1282187, 2566561.
%C a(21) > 22166. - _J.W.L. (Jan) Eerland_, Jul 25 2023
%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(k) = ispseudoprime(eval(Str(2^k, 3^k))); \\ _Michel Marcus_, Jan 26 2016, Sep 08 2021, Jul 15 2023
%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
%E a(20) from _Michael S. Branicky_, Apr 04 2023
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