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 A047847 #17 Jan 28 2023 16:49:59
%S A047847 1,3,6,9,18,21,33,39,48,51,54,63,81,96,111,114,138,153,156,174,189,
%T A047847 198,219,228,231,243,249,306,321,336,369,378,384,411,426,429,438,441,
%U A047847 453,468,483,504,543,546,606,639,648,651,711,714,723,741,744,774,783,789
%N A047847 Numbers n such that n + (n+1) and (n+2) + (n+3) are both prime.
%C A047847 Except for the first one, all terms are multiples of 3, as can be seen from the formula a(n+1) = 3*A056956(n). - _Zak Seidov_, Aug 26 2012
%H A047847 Jayanta Basu, <a href="/A047847/b047847.txt">Table of n, a(n) for n = 1..10000</a>
%F A047847 a(n) = (A023200(n)-1)/2 = (A046132(n)-5)/2 = 3*A056956(n-1) (for n>1).
%e A047847 If n = 6, then 6 + 7 = 13 and 8 + 9 = 17 are both prime.
%t A047847 Select[Range[790], And @@ PrimeQ[{2*# + 1, 2*# + 5}] &] (* _Jayanta Basu_, Aug 11 2013 *)
%t A047847 Select[Range[800],AllTrue[2#+{1,5},PrimeQ]&] (* _Harvey P. Dale_, Jan 28 2023 *)
%o A047847 (PARI) is_A047847(n)=isprime(n*2+1)&isprime(n*2+5) \\ - _M. F. Hasler_, Aug 26 2012
%Y A047847 Cf. A005097, A014545.
%K A047847 easy,nonn
%O A047847 1,2
%A A047847 _Enoch Haga_
%E A047847 Corrected by _Henry Bottomley_, Jul 18 2000