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 A232723 #15 Mar 15 2015 18:35:16
%S A232723 0,1,2,4,-1,8,-3,-2,16,-7,-6,-4,3,32,-15,-14,-12,7,-8,5,6,64,-31,-30,
%T A232723 -28,15,-24,13,14,-16,9,10,12,-5,128,-63,-62,-60,31,-56,29,30,-48,25,
%U A232723 26,28,-13,-32,17,18,20,-9,24,-11,-10,256,-127,-126,-124,63
%N A232723 Sequence (or tree) generated by these rules: 0 is in S, and if x is in S, then 2*x and 1 - x are in S, and duplicates are deleted as they occur.
%C A232723 Let S be the set of numbers defined by these rules: 0 is in S, and if x is in S, then 2*x and 1 - x are in S. Then S is the set of integers, which arise in generations. Deleting duplicates as they occur, the generations are given by g(1) = (0), g(2) = (1), g(3) = (2), g(4) = (4,-1), g(5) = (8,-3,-2), etc. Concatenating these gives A232723. Every integer occurs exactly once in S. The even integers occupy the positions given by the lower Wythoff sequence, A000201; the odds, by the upper Wythoff sequence, A001950. The positive integers occupy the positions given by A189035, and the positions of the nonpositives, by A189034.
%C A232723 Inverse beginning with 0: 1, 2, 3, 13, 4, 20, 21, 18, 6, 31, 32, 89, 33, 28, 29, 26, 9, 49, 50, 136, 51, 143, 144, 141, 53, 44, ..., . - _Robert G. Wilson v_, Jun 17 2014
%H A232723 Clark Kimberling, <a href="/A232723/b232723.txt">Table of n, a(n) for n = 1..10000</a>
%e A232723 Each x begets 2*x and 1 - x, and if either has already occurred it is deleted. Thus, 0 begets 1, which begets 2, which begets (4,-1), etc.
%t A232723 x = {0}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, 2*x, 1 - x}]]], {10}]; x (* _Peter J. C. Moses_, Nov 28 2013 *)
%t A232723 Nest[ DeleteDuplicates[ Flatten[ # /. a_Integer -> {2a, 1-a}]]&, {0}, 9] (* _Robert G. Wilson v_, Jun 17 2014 *)
%Y A232723 Cf. A232559, A226130, A226131, A000201, A189035.
%K A232723 sign,easy
%O A232723 1,3
%A A232723 _Clark Kimberling_, Nov 28 2013