A216847 Integers n such that 6n -/+ 1 and 30n -/+ 1 are all primes.

1, 2, 5, 77, 100, 110, 135, 170, 215, 338, 357, 385, 390, 467, 555, 593, 597, 688, 737, 758, 980, 1127, 1682, 1743, 1785, 2305, 2555, 3152, 3372, 3640, 3927, 3985, 4375, 4480, 4597, 4615, 4653, 4685, 5082, 5252, 5357, 5558, 6018, 6078, 6088, 6155, 7012, 7380

Offset: 1

Author

Zak Seidov, Dec 10 2012

Keywords

• nonn

Comments

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.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A002822 and A176114.

Programs

Mathematica

Select[Range[10000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] && PrimeQ[30 # - 1] && PrimeQ[30 # + 1] &] (* T. D. Noe, Dec 10 2012 *)
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 *)

PARI

{for(n=1,6000,if(isprime(p=6*n-1)&&isprime(p+2)&&isprime(q=30*n-1)&&isprime(q+2),print1(n",")))}