This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A158709 #40 Mar 05 2018 10:03:20
%S A158709 2,3,7,11,19,31,47,59,67,71,127,131,151,167,179,211,239,307,311,347,
%T A158709 379,431,439,467,479,547,571,587,607,619,631,647,727,739,787,811,839,
%U A158709 859,907,911,967,991,1039,1091,1231,1259,1319,1399,1427,1471,1511,1531,1559
%N A158709 Primes p such that p + ceiling(p/2) is prime.
%C A158709 Or, 2 along with primes p such that Sum_{x=1..p} (1 - (-1)^x*x) is prime. - _Juri-Stepan Gerasimov_, Jul 14 2009
%C A158709 Apart from the first term, primes of the form 4*k-1 such that 6*k-1 is also prime. - _Charles R Greathouse IV_, Nov 09 2011
%C A158709 If both p and q are in A158709 and p + q == 2 (mod 4), then A006370(A006370(p + q)) = A006370((p + q)/2) = 3*(p + q)/2 + 1 is the sum of the two primes p+ceiling(p/2) and q+ceiling(q/2). - _Roderick MacPhee_, Feb 23 2018
%H A158709 Vincenzo Librandi, <a href="/A158709/b158709.txt">Table of n, a(n) for n = 1..1000</a>
%t A158709 lst={};Do[p=Prime[n];If[PrimeQ[Ceiling[p/2]+p],AppendTo[lst,p]],{n,6!}];lst
%t A158709 Select[Prime@ Range@ 250, PrimeQ@ Ceiling[3#/2] &] (* _Vincenzo Librandi_, Apr 15 2013 and slightly modified by _Robert G. Wilson v_, Feb 26 2018 *)
%o A158709 (PARI) forprime(p=2,1e4,if(isprime(p+ceil(p/2)),print1(p", "))) \\ _Charles R Greathouse IV_, Nov 09 2011
%o A158709 (PARI) print1(2);forprime(p=3,1e4,if(p%4==3&&isprime(p\4*6+5),print1(", "p))) \\ _Charles R Greathouse IV_, Nov 09 2011
%Y A158709 Cf. A158708.
%K A158709 nonn,easy
%O A158709 1,1
%A A158709 _Vladimir Joseph Stephan Orlovsky_, Mar 24 2009
%E A158709 Corrected by _Charles R Greathouse IV_, Mar 18 2010