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A282136 Numbers n such that both 2^k*3^(n-k) - 1 and 2^(n-k)*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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

2 is in this sequence because 2^1*3^(2-1) - 1 = 5 is prime and 2^(2-1)*3^1 - 1 = 5 is prime.

3 is in this sequence because 2^1*3^(3-1) - 1 = 17 is prime and 2^(3-1)*3^1 - 1 = 11 is prime.

4 is in this sequence because 2^1*3^(4-1) - 1 = 53 is prime and 2^(4-1)*3^1 - 1 = 23 is prime.

5 is in this sequence because 2^2*3^(5-2) - 1 = 107 is prime and 2^(5-2)*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, n-1, if(isprime(3^(n-k)<<k - 1) && isprime(3^k<<(n-k) - 1), return(1))); 0 \\ Charles R Greathouse IV, Feb 21 2017

CROSSREFS

Sequence in context: A277187 A087797 A280619 * A153730 A140691 A316468

Adjacent sequences:  A282133 A282134 A282135 * A282137 A282138 A282139

KEYWORD

nonn,more

AUTHOR

Juri-Stepan Gerasimov, Feb 06 2017

EXTENSIONS

More terms from Michael De Vlieger, Feb 07 2017

STATUS

approved

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Last modified October 20 17:57 EDT 2018. Contains 316398 sequences. (Running on oeis4.)