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 A154669 #8 Jan 12 2019 20:44:55
%S A154669 12,282,642,1452,12162,17292,34842,98562,194682,233922,347772,383682,
%T A154669 410412,544962,749082,1071642,1302492,1421292,1503372,1685442,2794242,
%U A154669 3011052,3235962,3312732,3792252,3875322,4755522
%N A154669 Averages k of twin prime pairs such that 2*k^3 + 12*k^2 is a square.
%C A154669 (11,13) is a twin prime pair with average 12; sqrt(2*12^3 + 12*12^2) = 72.
%p A154669 a := proc (n) if isprime(n-1) = true and isprime(n+1) = true and type(sqrt(2*n^3+12*n^2), integer) = true then n else end if end proc: seq(a(n), n = 3 .. 5000000); # _Emeric Deutsch_, Jan 20 2009
%t A154669 a[n_]:=Sqrt[2*n^3+12*n^2];lst={};Do[If[Floor[a[n]]==a[n],If[PrimeQ[n-1]&&PrimeQ[n+1],AppendTo[lst,n]]],{n,9!}];lst
%t A154669 Select[Mean/@Select[Partition[Prime[Range[400000]],2,1],#[[2]]-#[[1]] == 2&],IntegerQ[Sqrt[2#^3+12#^2]]&] (* _Harvey P. Dale_, Sep 05 2017 *)
%Y A154669 Cf. A152811.
%K A154669 nonn
%O A154669 1,1
%A A154669 _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009
%E A154669 Extended by _Emeric Deutsch_, Jan 20 2009