OFFSET
1,1
COMMENTS
Infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 24 2011
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
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).
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrea Raffetti, Jul 11 2011
STATUS
approved