%I #9 Jun 14 2022 15:30:08

%S 4,5,6,8,9,10,12,15,18,21,25,27,28,30,33,35,36,38,39,42,45,48,50,51,

%T 54,57,60,63,66,72,75,78,80,81,84,85,87,88,90,93,98,99,102,105,108,

%U 111,113,114,115,117,120,123,126,129,132,135,138,140,141,144,147,150,153,155,156,159,162,165,168

%N 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.

%C Numbers k such that A237885(k) > 0.

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

%H Robert Israel, <a href="/A354834/b354834.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p N:= 1000: # for terms <= N

%p S:= {}:

%p P:= select(isprime, [seq(i,i=3..2*N,2)]):

%p nP:= nops(P):

%p for i from 1 to nP do

%p p:= P[i];

%p for j from i+1 to nP do

%p q:= P[j];

%p if p+q > 2*N then break fi;

%p r:= (p+q)/2;

%p if isprime(p+2*q) and isprime(2*p+q) then

%p S:= S union {r}

%p fi

%p od

%p od:

%p sort(convert(S,list));

%Y Cf. A237885.

%K nonn

%O 1,1

%A _Robert Israel_, Jun 07 2022