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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Subsequence of A127430. Cf. A000040.

Sequence in context: A285805 A141180 A176371 * A040987 A040180 A158754

Adjacent sequences: A284528 A284529 A284530 * A284532 A284533 A284534

Keyword

nonn

Author

Zak Seidov, Mar 28 2017

Status

approved