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%I #23 Aug 21 2020 12:13:54
%S 2,12,23,45,325,703,2705,3598,4218,7338,10698,13562,16478,16665,20195,
%T 25195,29678,32312,36228,51882,79628,83522,84513,84525,89453,100028,
%U 106710,107712,108868,114527,119142,145590,147758,151557,167155,173960,190547,192588
%N 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.
%C Infinite under Dickson's conjecture. - _Charles R Greathouse IV_, Jul 24 2011
%H Charles R Greathouse IV, <a href="/A192851/b192851.txt">Table of n, a(n) for n = 1..10000</a>
%e 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).
%t 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 *)
%t 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 *)
%o (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
%Y Subsequence of A191626 and hence A002822.
%Y Cf. A014574.
%K nonn
%O 1,1
%A _Andrea Raffetti_, Jul 11 2011
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