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 A177680 #11 Sep 26 2017 15:22:27
%S A177680 1,5,110,135,355,425,555,565,975,1045,1755,5530,6935,7355,8925,9240,
%T A177680 9555,10640,10850,11730,11830,12045,12350,12460,13130,13445,13655,
%U A177680 14590,15540,17050,19245,20795,22330,22825,26070,26910,28075,30585,30805
%N A177680 Numbers n such that 6n and 12n are both the average of twin prime pairs.
%C A177680 Conjecture: all terms but the first term are multiples of 5. - _Harvey P. Dale_, Sep 26 2017
%H A177680 Harvey P. Dale, <a href="/A177680/b177680.txt">Table of n, a(n) for n = 1..1000</a>
%F A177680 a(n)=A066388(n)/6.
%e A177680 a(1)=1 because 6*1-1=5, 6*1+1=7, 12*1-1=11 and 12*1+1=13 are all twin primes.
%t A177680 Select[Range[31000],AllTrue[Flatten[{6*#+{1,-1},12*#+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 26 2017 *)
%Y A177680 Cf. A014574.
%K A177680 nonn
%O A177680 1,2
%A A177680 _Juri-Stepan Gerasimov_, May 10 2010
%E A177680 Corrected (13590 removed, 13655 and 14590 inserted, 22725 replaced by 22825) by _R. J. Mathar_, May 15 2010