A144842 Numbers k such that the three numbers k+3, k-3 and k+5 are all prime.

8, 14, 26, 56, 104, 134, 176, 194, 236, 266, 566, 596, 656, 824, 1016, 1226, 1286, 1484, 1604, 1616, 1874, 2084, 2336, 2546, 2966, 3254, 3326, 3464, 3536, 3764, 3914, 3926, 4016, 4214, 4256, 4646, 4796, 5006, 5276, 5474, 5654, 5846, 5864, 6266, 6356, 6566

Offset: 1

Author

Giovanni Teofilatto, Sep 22 2008

Keywords

• easy
• nonn

Comments

Subset of A087695. - R. J. Mathar, Sep 24 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Triplet.

Crossrefs

Cf. A046138, A087695, A086801, A144840.

Programs

Mathematica

Select[Range[7000], And @@ PrimeQ[# + {-3, 3, 5}] &] (* Amiram Eldar, Apr 14 2022 *)

Python

from sympy import isprime
def ok(n): return n > 4 and isprime(n-3) and isprime(n+3) and isprime(n+5)
print(list(filter(ok, range(6567)))) # Michael S. Branicky, Aug 14 2021

Formula

a(n) = A046138(n) + 3. - R. J. Mathar, Sep 24 2008

Extensions

Definition edited and extended by R. J. Mathar, Sep 24 2008