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 A162001 #26 Sep 19 2024 08:32:14
%S A162001 5,11,17,41,101,311,347,641,857,1301,1427,1481,2237,2687,3461,3527,
%T A162001 4001,4787,8861,10457,11171,11777,13691,14627,19421,19991,21017,21557,
%U A162001 22271,24917,25997,26261,26681,26711,27737,29021,31511,32057,33347,35591
%N A162001 Initial members of prime triples (p, p+2, p+6) for which also the sum 3p+8 is prime.
%C A162001 A subsequence of A022004 (= initial members of prime triples (p, p+2, p+6)). - _Emeric Deutsch_, Jul 12 2009
%H A162001 Robert Israel, <a href="/A162001/b162001.txt">Table of n, a(n) for n = 1..10000</a>
%F A162001 a(n) == 5 (mod 6). - _Hugo Pfoertner_, Sep 06 2024
%F A162001 a(n) = (A376013(n) - 8)/3. - _Amiram Eldar_, Sep 06 2024
%F A162001 a(n) >> n log^4 n. - _Charles R Greathouse IV_, Sep 19 2024
%e A162001 (5,7,11) => 23 is prime.
%p A162001 a := proc (n) if isprime(n) = true and isprime(n+2) = true and isprime(n+6) = true and isprime(3*n+8) = true then n else end if end proc: seq(a(n), n = 1 .. 50000); # _Emeric Deutsch_, Jul 12 2009
%t A162001 Select[Select[Partition[Prime[Range[4000]], 3, 1], Differences[#] == {2, 4} &], PrimeQ[Total[#]] &][[;; , 1]] (* _Amiram Eldar_, Sep 06 2024 *)
%o A162001 (PARI) list(lim)=my(v=List(), p=5, q=7, s); forprime(r=11, lim+6, if(r-p==6 && q-p==2 && isprime(s=3*p+8), listput(v, p)); p=q; q=r); Vec(v) \\ _Charles R Greathouse IV_, Sep 19 2024
%Y A162001 Subsequence of A162001.
%Y A162001 Cf. A022004, A376013.
%K A162001 nonn
%O A162001 1,1
%A A162001 Milton L. Brown (miltbrown(AT)earthlink.net), Jun 24 2009
%E A162001 Definition corrected by _Emeric Deutsch_, Jul 12 2009
%E A162001 Extended by _Emeric Deutsch_, Jul 12 2009