A376013 Prime numbers of the form 3p+8 where p, p+2 and p+6 are prime numbers.

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

Author

Zak Seidov, Sep 06 2024

Keywords

• nonn

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.

Examples

			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;
...
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A162001, A104160.

Programs

Mathematica

Select[Total /@ Select[Partition[Prime[Range[3500]], 3, 1], Differences[#] == {2, 4} &], PrimeQ] (* Amiram Eldar, Sep 06 2024 *)

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

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