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 A268111 Integers k such that the concatenation of 2^k and 3^k is prime. 0
 0, 1, 3, 7, 8, 21, 23, 33, 51, 88, 96, 227, 287, 1231, 1924, 3035, 3614, 4598, 6112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS First five primes: 11, 23, 827, 1282187, 2566561. LINKS 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(n) = isok(n) = isprime(eval(Str(2^n, 3^n))); \\ Michel Marcus, Jan 26 2016 and Sep 08 2021 (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 * A244532 A037208 A102007 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 STATUS approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)