A231332 Primes p = prime(k) such that p - 2k and p + 2k are prime.

17, 23, 37, 89, 113, 151, 307, 463, 557, 643, 701, 761, 863, 911, 977, 1019, 1069, 1093, 1427, 1481, 1733, 1867, 2521, 2687, 2731, 2753, 3163, 3221, 3581, 3623, 3877, 4139, 4243, 4621, 4643, 4783, 4861, 4889, 4937, 5443, 5569, 5807, 5903, 6619, 6701, 6761, 6871

Offset

1,1

Comments

Corresponding values of k: 7, 9, 12, 24, 30, 36, 63, 90, 102, 117, 126, 135, 150. All except the first one, 7, are multiples of 3.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

17 is the seventh prime, and 17 - 2 * 7 = 3 and 17 + 2 * 7 = 31, both of which are prime, so 17 is in the sequence.
23 is the ninth prime, and 23 - 2 * 9 = 5 and 23 + 2 * 9 = 41, both of which are prime, so 23 is in the sequence.
29 is the tenth prime, and 29 - 2 * 10 = 9 and 29 + 2 * 10 = 49, neither of which is prime, so 29 is not in the sequence.

Mathematica

Reap[Sow[17]; Do[p = Prime[k]; If[PrimeQ[p + 2 * k] && PrimeQ[p - 2 * k], Sow[p]], {k, 9, 10^3, 3}]][[2, 1]]
Select[Table[{n, Prime[n]}, {n, 1000}], AllTrue[#[[2]]+{2#[[1]], -2#[[1]]}, PrimeQ]&][[All, 2]] (* Harvey P. Dale, Aug 05 2022 *)

Prog

(PARI){print(17", "); forstep(k=9, 885, 3, p=prime(k); if(isprime(p+2*k)&& isprime(p-2*k), print(p", ")))}
(PARI) k=0; forprime(p=2, 1e6, k++; if(isprime(p-2*k) && isprime(2+2*k), print1(p", "))) \\ Charles R Greathouse IV, Jan 07 2014

Crossrefs

Intersection of A231232 and A231326. Cf. A000040, A231506, A014689

Sequence in context: A333327 A241528 A156567 * A243137 A256397 A139843

Adjacent sequences: A231329 A231330 A231331 * A231333 A231334 A231335

Keyword

nonn

Author

Zak Seidov, Jan 07 2014

Status

approved