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 A225571 #12 Apr 04 2015 21:46:57
%S A225571 0,1,3,4,10,11,13,14,29,30,32,33,38,39,41,42,85,86,88,89,94,95,97,98,
%T A225571 112,113,115,116,122,123,125,238,248,251,252,255,257,260,261,273,275,
%U A225571 278,279,287,288,292,330,331,334,335
%N A225571 Lexicographically earliest sequence of nonnegative integers which does not contain a three-term arithmetic or geometric subsequence.
%C A225571 This sequence diverges from A224853 at 477th term. Here a(477) = 17380, while A224853(477) = 17408.
%H A225571 Giovanni Resta, <a href="/A225571/b225571.txt">Table of n, a(n) for n = 1..10000</a>
%e A225571 After terms 0, 1, 3, 4 have been added, the terms 5,...,9 are forbidden by subsequences (3,4,5), (0,3,6), (1,4,7), (0,4,8) and (1,3,9) so the next term is 10.
%t A225571 seq = {0, 1}; bad[n_] := Catch[ Do[If[MemberQ[seq, (n + e)/2], Throw@True], {e, seq}]; Do[If[MemberQ[seq, Sqrt[n*e]], Throw@True], {e, Rest@ seq}]; False]; While[Length[seq] < 100, x = Last[seq]+1; While[bad[x], x++]; AppendTo[seq, x]]; seq
%Y A225571 Cf. A224853, A003278, A005836, A000452.
%K A225571 nonn,look
%O A225571 1,3
%A A225571 _Giovanni Resta_, Jul 29 2013