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%I #37 Aug 23 2014 11:22:08
%S 1,2,5,77,100,110,135,170,215,338,357,385,390,467,555,593,597,688,737,
%T 758,980,1127,1682,1743,1785,2305,2555,3152,3372,3640,3927,3985,4375,
%U 4480,4597,4615,4653,4685,5082,5252,5357,5558,6018,6078,6088,6155,7012,7380
%N Integers n such that 6n -/+ 1 and 30n -/+ 1 are all primes.
%C Consider two primes P=2p+3q, Q=2q+3p with p and q twin primes, and p=6n-1, then P=Q+2, and sequence gives corresponding values of n.
%H Harvey P. Dale, <a href="/A216847/b216847.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[10000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] && PrimeQ[30 # - 1] && PrimeQ[30 # + 1] &] (* _T. D. Noe_, Dec 10 2012 *)
%t Select[Range[8000],AllTrue[Flatten[{6#+{1,-1},30#+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 23 2014 *)
%o (PARI){for(n=1,6000,if(isprime(p=6*n-1)&&isprime(p+2)&&isprime(q=30*n-1)&&isprime(q+2),print1(n",")))}
%Y Intersection of A002822 and A176114.
%K nonn
%O 1,2
%A _Zak Seidov_, Dec 10 2012