A242366 Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p is prime.

2, 3, 11, 59, 131, 179, 347, 1259, 1571, 1979, 2027, 2411, 2699, 2819, 3251, 3347, 4211, 5051, 5099, 5171, 5531, 6779, 7187, 8747, 10091, 12227, 13259, 13451, 13499, 13931, 14411, 14771, 15131, 15467, 16451, 16691, 17987, 18131, 18539, 18731, 18899, 19211

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

Cf. A158714.

Sequence in context: A353727 A041441 A110482 * A105217 A066046 A065597

Adjacent sequences: A242363 A242364 A242365 * A242367 A242368 A242369

Keyword

nonn

Author

Robert Israel and Vladimir Joseph Stephan Orlovsky, May 11 2014

Status

approved