A350856 Initial members of prime triples (p, p+2, p+14).

3, 5, 17, 29, 59, 137, 149, 179, 197, 227, 269, 419, 599, 617, 659, 809, 1019, 1049, 1277, 1289, 1607, 1787, 1997, 2129, 2237, 2267, 2657, 2789, 3167, 3257, 3299, 3329, 3359, 3527, 3557, 3917, 3929, 4217, 4229, 4259, 4547, 4637, 4649, 4787, 4799, 5009, 5099

Offset: 1

Author

Matt C. Anderson, Jan 19 2022

Keywords

• nonn

Comments

According to the k-tuple conjecture this sequence is theoretically infinite.

Links

• Chris K. Caldwell prime k-tuple conjecture
• Chris K. Caldwell k-tuple

Crossrefs

Cf. A022004 (p,p+2,p+6), A046134 (p,p+2,p+8), A046135 (p,p+2,p+12).

Programs

Maple

for a from 3 to 1000 by 2 do
if isprime(a) and isprime(a+2) and isprime(a+14) then
print(a);
end if
end do
# second Maple program:
q:= p-> andmap(isprime, [p, p+2, p+14]):
select(q, [$1..10000])[];  # Alois P. Heinz, Jan 28 2022

Mathematica

Select[Range[7000], And @@ PrimeQ[# + {0, 2, 14}] &] (* Amiram Eldar, Jan 20 2022 *)