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A192851
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Integers n such that 6n, 36n, and 216n fall between pairs of twin primes, that is, 6n-1, 6n+1, 36n-1, 36n+1, 216n-1, and 216n+1 are prime.
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2
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2, 12, 23, 45, 325, 703, 2705, 3598, 4218, 7338, 10698, 13562, 16478, 16665, 20195, 25195, 29678, 32312, 36228, 51882, 79628, 83522, 84513, 84525, 89453, 100028, 106710, 107712, 108868, 114527, 119142, 145590, 147758, 151557, 167155, 173960, 190547, 192588
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OFFSET
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1,1
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COMMENTS
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Infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 24 2011
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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EXAMPLE
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12 is in the list because 12*6=72, 12*36=432, 12*216=2592 are all between a pair of twin primes (71,73 and 431,433 and 2591,2593).
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MATHEMATICA
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Select[Range[1000000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] && PrimeQ[36 # - 1] && PrimeQ[36 # + 1] && PrimeQ[216 # - 1] && PrimeQ[216 # + 1] &] (* T. D. Noe, Jul 26 2011 *)
Select[Range[193000], AllTrue[{6#-1, 6#+1, 36#-1, 36#+1, 216#-1, 216#+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 21 2020 *)
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PROG
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(PARI) is(n)=isprime(6*n-1) && isprime(6*n+1) && isprime(36*n-1) && isprime(36*n+1) && isprime(216*n-1) && isprime(216*n+1) \\ Charles R Greathouse IV, Sep 15 2015
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CROSSREFS
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Subsequence of A191626 and hence A002822.
Cf. A014574.
Sequence in context: A012664 A012545 A009514 * A112718 A117301 A141079
Adjacent sequences: A192848 A192849 A192850 * A192852 A192853 A192854
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KEYWORD
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nonn
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AUTHOR
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Andrea Raffetti, Jul 11 2011
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STATUS
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approved
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