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URL: https://oeis.org/A391321

⇱ A391321 - OEIS

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A391321
Primes of the form 3*p+2 in which p and p+2 are twin primes.
1
11, 17, 53, 89, 179, 449, 593, 683, 719, 809, 1259, 1709, 1979, 3833, 4283, 4463, 5003, 5849, 6263, 6389, 6803, 7019, 7649, 8369, 8999, 10079, 10169, 11789, 12149, 12473, 12653, 12689, 13553, 13913, 15299, 16253, 16433, 18269, 18593, 18899, 19079, 19709, 19979, 20483, 20879, 21383
OFFSET
1,1
COMMENTS
This sequence is the image of A174913 under the linear map p -> 3p + 2, where p is the smaller member of a twin prime pair (p,p+2) such that 3p+2 is prime.
LINKS
FORMULA
a(n) = 3*A174913(n) + 2.
EXAMPLE
A174913 begins 3, 5, 17, 29, 59, ...
Applying p -> 3*p + 2 gives:
p = 3 -> a(1) = 3*3 + 2 = 11.
p = 5 -> a(2) = 3*5 + 2 = 17.
p = 17 -> a(3) = 3*17 + 2 = 53.
p = 29 -> a(4) = 3*29 + 2 = 89.
p = 59 -> a(5) = 3*59 + 2 = 179.
MATHEMATICA
Select[3*Select[Prime[Range[1000]], PrimeQ[# + 2] &] + 2, PrimeQ] (* Paolo Xausa, Dec 13 2025 *)
PROG
(Python)
from sympy import isprime
A = []
p = 3
while len(A) < 60:
if isprime(p) and isprime(p+2) and isprime(3*p+2):
A.append(3*p+2)
p += 2
print(A)
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
p, q = 3, 5
while True:
if q-p == 2 and isprime(r:=3*p+2): yield r
p, q = q, nextprime(q)
print(list(islice(agen(), 46))) # Michael S. Branicky, Dec 07 2025
(PARI) apply(x->3*x+2, select(x->(isprime(x) && isprime(x+2) && isprime(3*x+2)), primes(1000))) \\ Michel Marcus, Dec 07 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Bruce Nye, Dec 06 2025
STATUS
approved