A377406 Primes which are sums of a prime triple (p, p+4, p+6).

31, 211, 1381, 3271, 4999, 6421, 8059, 9769, 10399, 11551, 16249, 20479, 23269, 23629, 27031, 28309, 33349, 35491, 39019, 54139, 63949, 70879, 106591, 109579, 116131, 127219, 130729, 141439, 142969, 150151, 151771, 153589, 163741, 167449, 169591, 195511, 205339, 208489, 210361, 216679, 222601, 224149

Offset: 1

Author

James S. DeArmon, Oct 27 2024

Keywords

• nonn

Comments

The prime triple herein is restricted to the form (p, p+4, p+6). In number theory, the other form of a prime triple is (p, p+2, p+6).

Equivalently, primes of the form 3*A022005(k) + 10.

Examples

			The first term is 31, the sum of the triple (7, 11, 13).
The second term is 211, the sum of the triple (67, 71, 73).
		

Crossrefs

Cf. A022005, A162001, A376013.

Subset of A002476.

Programs

Maple

q:= p-> andmap(isprime, (t->[p, t, t-4, t+2])((p+2)/3)):
select(q, [6*i+1$i=1..50000])[];  # Alois P. Heinz, Nov 13 2024

Mathematica

Select[Total /@ Select[Partition[Prime[Range[7500]], 3, 1], Differences[#] == {4, 2} &], PrimeQ] (* Amiram Eldar, Oct 31 2024 *)

Python

from sympy import isprime
sums = set()
for n in range(100000):
    if isprime(n) and isprime(n+4) and isprime(n+6) and isprime(3*n+10):
            sums.add(3*n+10)
print(sorted(sums))

Formula

a(n) mod 6 = 1.