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 A153778 #6 Mar 30 2012 18:51:00
%S A153778 1,1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,
%T A153778 1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,
%U A153778 1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1
%N A153778 Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation.
%C A153778 The Jacobsthal sequence gives numbers of zeros and ones in the rows of the tree:
%C A153778 A001045(k) = #{i: 2^k <= i < 2^(k+1) and a(i)=0};
%C A153778 A001045(k+1) = #{i: 2^k <= i < 2^(k+1) and a(i)=1}.
%H A153778 N. J. A. Sloane, <a href="/stern_brocot.html">Stern-Brocot or Farey Tree</a>
%H A153778 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A153778 a(1) = 1 and for n>1: a(n) = if A025480(n-1)<>0 and A025480(n)<>0 then a(A025480(n-1)) XOR a(A025480(n)) else if A025480(n)=0 then 1-a(A025480(n-1)) else a(A025480(n-1)).
%e A153778 .[0] . . . . . . . . . . . . . . . . . [1]
%e A153778 ................... 1
%e A153778 ........... 1 ............. 0
%e A153778 ....... 1 ..... 0 ..... 1 ..... 1
%e A153778 ..... 1 . 0 . 1 . 1 . 0 . 1 . 1 . 0
%e A153778 .... 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1.
%K A153778 nonn,tabf
%O A153778 1,1
%A A153778 _Reinhard Zumkeller_, Jan 01 2009