A158714 Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime.

3, 19, 67, 307, 379, 467, 547, 587, 739, 859, 1259, 1699, 1747, 1867, 2027, 2699, 2819, 3259, 3539, 4019, 4507, 5059, 5779, 7547, 8219, 8539, 8747, 8819, 9547, 10067, 10499, 10667, 11939, 13259, 13627, 13859, 14939, 17659, 17707, 17987, 18859

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 24 2009

Keywords

• nonn

Comments

All a(n) == 3 (mod 8), as this is necessary for p, p1 and p2 to be odd. - Robert Israel, May 11 2014

Examples

			67 is in the sequence because 67, ceiling(67/2) + 67 = 101 and floor(101/2) + 101 = 151 are all primes.
		

Links

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

Crossrefs

Cf. A158708, A158709, A158710, A158711, A158712, A158713, A242366.

Programs

Maple

N:= 10^5; # to get all entries <= 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)+p1;
     isprime(p2);
end proc;
select(filter,[seq(2*i+1,i=1..floor((N-1)/2)]; # Robert Israel, May 09 2014

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p=Ceiling[p/2]+p],If[PrimeQ[p=Floor[p/2]+p],AppendTo[lst,Prime[n]]]],{n,7!}];lst

Extensions

Definition corrected by Robert Israel, May 09 2014