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 A158351 #9 Apr 23 2024 11:27:23
%S A158351 3,251,523,1063,4007,4373,4423,7517,11801,11833,11927,12491,12757,
%T A158351 12967,15817,15907,16381,16481,16763,16987,17851,21341,21937,22343,
%U A158351 22441,22877,23327,25849,26591,26993,27061,31153,31321,31583,33773,35159
%N A158351 Primes p0 such that p0+p1+p2-+2 are primes; p0,p1,p2 are three consecutive primes.
%C A158351 sum of three consecutive primes = arithmetical mean of two primes. 3+5+7=15-+2 (13,17)primes, 251+257+263-+2 (769,773)primes, ...
%H A158351 Harvey P. Dale, <a href="/A158351/b158351.txt">Table of n, a(n) for n = 1..1000</a>
%t A158351 lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];a=p0+p1+p2;If[PrimeQ[a-2]&&PrimeQ[a+2],AppendTo[lst,p0]],{n,2*7!}];lst
%t A158351 Select[Partition[Prime[Range[4000]],3,1],AllTrue[Total[#]+{2,-2},PrimeQ]&][[;;,1]] (* _Harvey P. Dale_, Apr 23 2024 *)
%o A158351 (PARI) is(n)=my(p=nextprime(n+1),q=nextprime(p+1)); isprime(n) && isprime(n+p+q-2) && isprime(n+p+q+2) \\ _Charles R Greathouse IV_, Jan 29 2016
%Y A158351 Cf. A099349, A158350.
%K A158351 nonn
%O A158351 1,1
%A A158351 _Vladimir Joseph Stephan Orlovsky_, Mar 16 2009