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

%I A158714 #26 Nov 17 2019 01:45:41
%S A158714 3,19,67,307,379,467,547,587,739,859,1259,1699,1747,1867,2027,2699,
%T A158714 2819,3259,3539,4019,4507,5059,5779,7547,8219,8539,8747,8819,9547,
%U A158714 10067,10499,10667,11939,13259,13627,13859,14939,17659,17707,17987,18859
%N A158714 Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime.
%C A158714 All a(n) == 3 (mod 8), as this is necessary for p, p1 and p2 to be odd. - _Robert Israel_, May 11 2014
%H A158714 Robert Israel, <a href="/A158714/b158714.txt">Table of n, a(n) for n = 1..10000</a>
%e A158714 67 is in the sequence because 67, ceiling(67/2) + 67 = 101 and floor(101/2) + 101 = 151 are all primes.
%p A158714 N:= 10^5; # to get all entries <= N
%p A158714 filter:= proc(p)
%p A158714      local p1,p2;
%p A158714      if not isprime(p) then return false fi;
%p A158714      p1:= ceil(p/2)+p;
%p A158714      if not isprime(p1) then return false fi;
%p A158714      p2:= floor(p1/2)+p1;
%p A158714      isprime(p2);
%p A158714 end proc;
%p A158714 select(filter,[seq(2*i+1,i=1..floor((N-1)/2)]; # _Robert Israel_, May 09 2014
%t A158714 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
%Y A158714 Cf. A158708, A158709, A158710, A158711, A158712, A158713, A242366.
%K A158714 nonn
%O A158714 1,1
%A A158714 _Vladimir Joseph Stephan Orlovsky_, Mar 24 2009
%E A158714 Definition corrected by _Robert Israel_, May 09 2014