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A282136
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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.
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0
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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
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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