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 A233696 #20 May 06 2017 13:12:02
%S A233696 1,2,3,5,10,11,18,23,30,49,56,102,109,212,219,443,450,926,933,1939,
%T A233696 1946,4064,4071,8509,8516,17816,17823,37303,37310,78105,78112,163544,
%U A233696 163551
%N A233696 Positions of integers in the sequence (or tree) S generated in order by these rules: 0 is in S; if x is in S then x + 1 is in S; if nonzero x is in S then 1/x is in S; if x is in S, then i*x is in S; where duplicates are deleted as they occur.
%C A233696 It can be proved using the division algorithm for Gaussian integers that S is the set of Gaussian rational numbers: (b + c*i)/d, where b,c,d are integers and d is not 0.
%e A233696 The first 16 numbers generated are as follows: 0, 1, 2, i, 3, 1/2, 2 i, 1 + i, -i, -1, 4, 1/3, 3 i, 3/2, i/2, 1 + 2 i. Positions of integers 0, 1, 2, 3, -1, 4,... are 1,2,3,5,10,11,....
%t A233696 Off[Power::infy]; x = {0}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 1/x, I*x} /. ComplexInfinity -> 0]]], {18}]; On[Power::infy]; t1 = Flatten[Position[x, _?(IntegerQ[#] && NonNegative[#] &)]] (*A233694*)
%t A233696 t2 = Flatten[Position[x, _?(IntegerQ[#] && Negative[#] &)]] (*A233695*)
%t A233696 t = Union[t1, t2] (*A233696*)
%t A233696 (* _Peter J. C. Moses_, Dec 21 2013 *)
%Y A233696 Cf. A233694, A233695, A232559, A226130, A232723, A226080.
%K A233696 nonn,more
%O A233696 1,2
%A A233696 _Clark Kimberling_, Dec 19 2013
%E A233696 Definition and example corrected. - _R. J. Mathar_, May 06 2017