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 A233559 #14 Nov 26 2016 11:37:43
%S A233559 1,2,3,4,6,9,5,8,12,7,18,10,27,15,16,24,13,36,14,21,19,54,11,20,30,28,
%T A233559 81,45,17,32,48,25,72,26,39,37,108,42,22,63,38,57,55,162,33,40,60,31,
%U A233559 90,29,56,84,82,243,46,135,34,51,64,96,49,144,50,75,73
%N A233559 Tree read by levels generated by these rules: 1 is at the top, and the node x has child nodes x+1, 2*x, and 3*x, where duplicates are deleted as they occur.
%C A233559 Every positive integer occurs exactly once in S, so that S is a permutation of the natural numbers. Deleting duplicates as they occur, the generations of S are given by g(1) = (1), g(2) = (2,3), g(3) = (4,6,9), g(4) = (5,8,12,7,18,10,27), ... Concatenating gives 1,2,3,4,6,9,5,...
%H A233559 Clark Kimberling, <a href="/A233559/b233559.txt">Table of n, a(n) for n = 1..5000</a>
%e A233559 To generate S, start with g(1) = (1). Then 1 begets 2 and 3; then 2 begets 4 and 3 begets 6 and 9.
%t A233559 x = {1}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 2 x, 3 x}]]], {8}]; x (* A233559 *)
%t A233559 y = Flatten[Table[Position[x, n], {n, 1, 157}]] (* A233560 *)
%Y A233559 Cf. A232559, A233560.
%K A233559 nonn,easy
%O A233559 1,2
%A A233559 _Clark Kimberling_, Dec 14 2013
%E A233559 Name edited by _Ivan Neretin_, Nov 26 2016