A192851 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.

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

Offset: 1

Author

Andrea Raffetti, Jul 11 2011

Keywords

• nonn

Comments

Infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 24 2011

Examples

			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).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A191626 and hence A002822.

Cf. A014574.

Programs

Mathematica

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 *)

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