A354834 Numbers k such that 2*k can be written in at least one way as p+q with p, q, p+2*q and 2*q+p all prime.

4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 25, 27, 28, 30, 33, 35, 36, 38, 39, 42, 45, 48, 50, 51, 54, 57, 60, 63, 66, 72, 75, 78, 80, 81, 84, 85, 87, 88, 90, 93, 98, 99, 102, 105, 108, 111, 113, 114, 115, 117, 120, 123, 126, 129, 132, 135, 138, 140, 141, 144, 147, 150, 153, 155, 156, 159, 162, 165, 168

Offset: 1

Author

Robert Israel, Jun 07 2022

Keywords

• nonn

Comments

Numbers k such that A237885(k) > 0.

If k is not divisible by 3, then p or q must be 3.

Examples

			a(3) = 6 is a term because 2*6 = 12 = 5+7 with 5, 7, 5+2*7 = 19 and 2*5+7 = 17 all prime.
		

Links

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

Crossrefs

Cf. A237885.

Programs

Maple

N:= 1000: # for terms <= N
S:= {}:
P:= select(isprime, [seq(i,i=3..2*N,2)]):
nP:= nops(P):
for i from 1 to nP do
  p:= P[i];
  for j from i+1 to nP do
    q:= P[j];
    if p+q > 2*N then break fi;
    r:= (p+q)/2;
    if isprime(p+2*q) and isprime(2*p+q) then
      S:= S union {r}
    fi
  od
od:
sort(convert(S,list));