A284531 Primes p such that 6p - 5 and 6p + 5 are consecutive primes.

31, 41, 71, 97, 139, 193, 337, 349, 421, 487, 587, 619, 643, 701, 811, 827, 1021, 1051, 1093, 1217, 1249, 1259, 1471, 1571, 1721, 1747, 1861, 1949, 2087, 2131, 2383, 2521, 2549, 2591, 2957, 3023, 3083, 3209, 3529, 3613, 3779, 3833, 3947, 4283, 4409, 4451, 4481, 4483, 4567, 4591, 4733

Offset: 1

Author

Zak Seidov, Mar 28 2017

Keywords

• nonn

Comments

a(n + 1) = a(n) + 2 for n = 47, 386, 868, 1000, 1247, 1521, 1834, 2271, 2435, 2437, 2468, 2483, 2811, 2819, 2960, 3202, 3531, 3581, 5021, 5178, 5245, 5669, 6009, 6087, 6198, 6686, 7017, 7029, 7454, 7576, 7699, 8557, 8940, 9018, 10130, 10240, 10449, 10578, 10952, 11070, 11103, 11199, ...

E.g., a(42)=4481 and a(43)=4483.

Examples

			31*6 - 5 = 181 = A000040(42) and 31*6 + 5 = 191 = A000040(43).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A127430. Cf. A000040.

Programs

Maple

filter:= p -> isprime(p) and isprime(6*p-5) and isprime(6*p+5) and not isprime(6*p-1) and not isprime(6*p+1):
select(filter, [seq(i,i=3..10000, 2)]); # Robert Israel, Apr 07 2017

Mathematica

Select[Range[31,5000,2], PrimeQ[#] && PrimeQ[a = 6 # - 5] && NextPrime[a] == a + 10 &]
cp6Q[n_]:=Module[{p1=6n-5},PrimeQ[p1]&&NextPrime[p1]==6n+5]; Select[ Prime[ Range[ 1000]],cp6Q] (* Harvey P. Dale, Jun 05 2017 *)