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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 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)<

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)