OFFSET
1,1
COMMENTS
All terms after 2 are congruent to 3 mod 8, as this is needed for p, p1 and p2 to be odd. If p = 3 + 8*k, then p1 = 5 + 12*k and p2 = 5 + 14*k.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
11 is in the sequence since 11, ceiling(11/2) + 11 = 17 and floor(17/2) + 11 = 19 are all primes.
MAPLE
N:= 100000: # to get all terms <= N
filter:= proc(p) local p1, p2;
if not isprime(p) then return false fi;
p1:= ceil(p/2)+p;
if not isprime(p1) then return false fi;
p2:= floor(p1/2)+p;
isprime(p2);
end;
select(filter, [2, seq(3+8*k, k=0 .. floor((N-3)/8))]);
MATHEMATICA
M = 100000;
filterQ[p_] := Module[{p1, p2},
If[!PrimeQ[p], Return[False]];
p1 = Ceiling[p/2] + p;
If[!PrimeQ[p1], Return[False]];
p2 = Floor[p1/2] + p;
PrimeQ[p2]];
Select[Join[{2}, Table[3+8*k, {k, 0, Floor[(M-3)/8]}]], filterQ] (* Jean-François Alcover, Apr 27 2019, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel and Vladimir Joseph Stephan Orlovsky, May 11 2014
STATUS
approved