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

1,1

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.

Links

Table of n, a(n) for n=1..42.

Formula

a(n) mod 6 = 1.

Example

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).

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 *)

Prog

(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))

Crossrefs

Cf. A022005, A162001, A376013.

Subset of A002476.

Sequence in context: A090027 A164784 A290008 * A121616 A284899 A062393

Adjacent sequences: A377403 A377404 A377405 * A377407 A377408 A377409

Keyword

nonn

Author

James S. DeArmon, Oct 27 2024

Status

approved