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 A127558 #4 Mar 31 2012 10:22:03
%S A127558 2,9,0,0,0,6,9,4,9,2,6,9,1,7,9,8,0,1,4,4,2,3,7,1,3,5,8,1,4,0,8,7,8,4,
%T A127558 9,1,2,0,4,8,7,4,8,2,8,7,5,9,7,5,7,3,4,7,7,9,8,4,2,5,9,3,4,4,6,1,5,1,
%U A127558 6,0,6,4,5,0,8,6,1,3,6,3,8,3,5,5,3,0,0,3,0,9,5,0,0,9,6,7,2,9,5,6
%N A127558 Decimal expansion of the number 29.000694926917980144237135814... having continued fraction expansion 29, 1439, 4211, 7703, 12907, 14957, ... (A126555).
%t A127558 b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 100000}];Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a] - 1}]; RealDigits[N[FromContinuedFraction[b], 100]][[1]]
%Y A127558 Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127559, A126555.
%K A127558 cons,nonn
%O A127558 2,1
%A A127558 _Artur Jasinski_, Jan 18 2007
%E A127558 Offset corrected by _R. J. Mathar_, Feb 05 2009