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

1,2

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

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 *)

Prog

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

Crossrefs

Intersection of A002822 and A176114.

Sequence in context: A128297 A183291 A254405 * A102983 A038583 A082080

Adjacent sequences: A216844 A216845 A216846 * A216848 A216849 A216850

Keyword

nonn

Author

Zak Seidov, Dec 10 2012

Status

approved