A376013 -id:A376013 - cp's OEIS frontend

A162001 Initial members of prime triples (p, p+2, p+6) for which also the sum 3p+8 is prime.

5, 11, 17, 41, 101, 311, 347, 641, 857, 1301, 1427, 1481, 2237, 2687, 3461, 3527, 4001, 4787, 8861, 10457, 11171, 11777, 13691, 14627, 19421, 19991, 21017, 21557, 22271, 24917, 25997, 26261, 26681, 26711, 27737, 29021, 31511, 32057, 33347, 35591

Offset: 1

Milton L. Brown (miltbrown(AT)earthlink.net), Jun 24 2009

nonn

A subsequence of A022004 (= initial members of prime triples (p, p+2, p+6)). - Emeric Deutsch, Jul 12 2009

			(5,7,11) => 23 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Subsequence of A162001.

Cf. A022004, A376013.

a := proc (n) if isprime(n) = true and isprime(n+2) = true and isprime(n+6) = true and isprime(3*n+8) = true then n else end if end proc: seq(a(n), n = 1 .. 50000); # Emeric Deutsch, Jul 12 2009

Select[Select[Partition[Prime[Range[4000]], 3, 1], Differences[#] == {2, 4} &], PrimeQ[Total[#]] &][[;; , 1]] (* Amiram Eldar, Sep 06 2024 *)

list(lim)=my(v=List(), p=5, q=7, s); forprime(r=11, lim+6, if(r-p==6 && q-p==2 && isprime(s=3*p+8), listput(v, p)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Sep 19 2024

a(n) == 5 (mod 6). - Hugo Pfoertner, Sep 06 2024
a(n) = (A376013(n) - 8)/3. - Amiram Eldar, Sep 06 2024
a(n) >> n log^4 n. - Charles R Greathouse IV, Sep 19 2024

Definition corrected by Emeric Deutsch, Jul 12 2009

Extended by Emeric Deutsch, Jul 12 2009

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

Original entry on oeis.org

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

James S. DeArmon, Oct 27 2024

nonn

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.

			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).

Cf. A022005, A162001, A376013.

Subset of A002476.

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

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

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))

a(n) mod 6 = 1.

cp's OEIS Frontend

A162001 Initial members of prime triples (p, p+2, p+6) for which also the sum 3p+8 is prime.

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