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 A133771 #13 Sep 29 2018 18:45:37 %S A133771 2,1,1,2,3,1,3,2,3,1,4,5,3,3,2,3,1,5,4,5,3,4,5,3,3,2,3,1,6,7,5,5,4,5, %T A133771 3,5,4,5,3,4,5,3,3,2,3,1,7,6,7,5,6,7,5,5,4,5,3,6,7,5,5,4,5,3,5,4,5,3, %U A133771 4,5,3,3,2,3,1,8,9,7,7,6,7,5,7,6,7,5,6,7,5,5,4,5,3,7,6,7,5,6,7,5,5,4,5,3,6 %N A133771 Number of runs (of equal bits) in the maximal Lucas binary (A130311) representation of n. %D A133771 Zeckendorf, E., Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41, 179-182, 1972. %H A133771 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phigits.html">Using Powers of Phi to represent Integers</a>. %e A133771 A130311(19)=101110 because 11+4+3+1=19 (a sum of Lucas numbers); this representation has four runs: 1,0,111,0. So a(19)=4. %Y A133771 Cf. A133770, A130311. %K A133771 nonn %O A133771 1,1 %A A133771 _Casey Mongoven_, Sep 23 2007; corrected Mar 23 2008 %E A133771 The b-file submitted by Casey Mongoven did not match the terms of the sequence, so I have deleted it. Of course it may be that the sequence is wrong and the b-file was correct. Should be rechecked. - _N. J. A. Sloane_, Nov 10 2010