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A216847 Integers n such that 6n -/+ 1 and 30n -/+ 1 are all primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 11:14 EDT 2017. Contains 287204 sequences.