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A376013
Prime numbers of the form 3p+8 where p, p+2 and p+6 are prime numbers.
3
23, 41, 59, 131, 311, 941, 1049, 1931, 2579, 3911, 4289, 4451, 6719, 8069, 10391, 10589, 12011, 14369, 26591, 31379, 33521, 35339, 41081, 43889, 58271, 59981, 63059, 64679, 66821, 74759, 77999, 78791, 80051, 80141, 83219, 87071, 94541, 96179
OFFSET
1,1
COMMENTS
An integer n is in this list if it is a prime number and (n-8)/3, (n-2)/3, (n+10)/3 are all prime numbers. 23 is a term because it is prime and 5, 7 and 11 are prime numbers.
LINKS
FORMULA
a(n) = 3*A162001(n) + 8. - Daniel Mondot, Sep 06 2024
a(n) == 5 (mod 6). - Hugo Pfoertner, Sep 06 2024
a(n) >> n log^4 n. - Charles R Greathouse IV, Sep 18 2024
EXAMPLE
5 + 7 + 11 = 23;
11 + 13 + 17 = 41;
17 + 19 + 23 = 59;
41 + 43 + 47 = 131;
101 + 103 + 107 = 311;
311 + 313 + 317 = 941;
347 + 349 + 353 = 1049;
...
MATHEMATICA
Select[Total /@ Select[Partition[Prime[Range[3500]], 3, 1], Differences[#] == {2, 4} &], PrimeQ] (* Amiram Eldar, Sep 06 2024 *)
PROG
(PARI) list(lim)=my(v=List(), p=5, q=7, s); forprime(r=11, (lim+10)\3, if(r-p==6 && q-p==2 && isprime(s=3*p+8), listput(v, s)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Sep 18 2024
CROSSREFS
Sequence in context: A115699 A301623 A163635 * A083444 A153037 A106970
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 06 2024
STATUS
approved