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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

Table of n, a(n) for n=1..19.

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.)