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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A175914.

Sequence in context: A191086 A058302 A133213 * A138465 A006598 A245623

Adjacent sequences: A368688 A368689 A368690 * A368692 A368693 A368694

Keyword

nonn

Author

Zak Seidov and Robert Israel, Jan 03 2024

Status

approved