A368691 Primes p such that p + 4 * q is prime, where q is the next prime after p.

3, 23, 31, 73, 83, 157, 167, 211, 251, 353, 373, 443, 467, 503, 509, 523, 541, 571, 647, 727, 751, 941, 947, 977, 1033, 1069, 1123, 1201, 1259, 1361, 1381, 1493, 1511, 1531, 1553, 1613, 1759, 1811, 2011, 2207, 2333, 2351, 2383, 2399, 2417, 2543, 2777, 2927, 3061, 3067, 3083, 3301, 3331, 3511

Offset: 1

Author

Zak Seidov and Robert Israel, Jan 03 2024

Keywords

• nonn

Examples

			a(3) = 31 is a term because 31 is prime, the next prime is 37, and 31 + 4 * 37 = 179 is prime.
		

Links

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

Crossrefs

Cf. A175914.

Programs

Maple

filter:= proc(p) local q;
  if not isprime(p) then return false fi;
  q:= nextprime(p);
  isprime(p+4*q)
end proc:
select(filter, [seq(i,i=3..10000,2)]);

Mathematica

f[p_] := Module[{q}, If[!PrimeQ[p], Return[False]]; q = NextPrime[p]; PrimeQ[p + 4*q]];Select[Range[3,3511, 2],f] (* James C. McMahon, Jan 03 2024 *)