

A282136


Numbers n such that both 2^k*3^(nk)  1 and 2^(nk)*3^k  1 are primes for some positive k < n.


0



2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 20, 23, 25, 31, 43, 47, 85, 101, 117, 173, 224, 277, 281, 349, 359, 365, 403, 521, 629, 691, 709, 819, 1037
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..33.


EXAMPLE

2 is in this sequence because 2^1*3^(21)  1 = 5 is prime and 2^(21)*3^1  1 = 5 is prime.
3 is in this sequence because 2^1*3^(31)  1 = 17 is prime and 2^(31)*3^1  1 = 11 is prime.
4 is in this sequence because 2^1*3^(41)  1 = 53 is prime and 2^(41)*3^1  1 = 23 is prime.
5 is in this sequence because 2^2*3^(52)  1 = 107 is prime and 2^(52)*3^2  1 = 71 is prime.


MATHEMATICA

Select[Range@ 800, Function[n, Total@ Boole@ Table[PrimeQ@ {2^k*3^(n  k)  1 , 2^(n  k)*3^k  1} == {True, True}, {k, n/2}] > 0]] (* Michael De Vlieger, Feb 07 2017 *)


PROG

(PARI) is(n)=for(k=1, n1, if(isprime(3^(nk)<<k  1) && isprime(3^k<<(nk)  1), return(1))); 0 \\ Charles R Greathouse IV, Feb 21 2017


CROSSREFS

Sequence in context: A277187 A087797 A280619 * A153730 A140691 A099627
Adjacent sequences: A282133 A282134 A282135 * A282137 A282138 A282139


KEYWORD

nonn,more


AUTHOR

JuriStepan Gerasimov, Feb 06 2017


EXTENSIONS

More terms from Michael De Vlieger, Feb 07 2017


STATUS

approved



