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 A308293 #13 May 23 2019 01:37:11 %S A308293 1,2,1,1,1,2,3,1,1,3,1,4,1,1,4,5,1,1,5,1,2,4,6,1,1,6,1,4,6,2,1,6,2,7, %T A308293 1,1,7,1,8,1,1,8,3,1,7,8,1,2,5,8,1,9,1,1,9,3,1,8,9,1,3,6,10,1,1,10,1, %U A308293 5,8,2,10,1,8,10,1,11,1,1,11,4,1,9,10,1 %N A308293 Lexicographically earliest sequence of positive terms such that a(1) = 1, a(2) = 2, and for any n > 0, (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) is unique. %C A308293 This sequence shows chaotic behavior (see scatterplot in Links section). %C A308293 This behavior is determined by the choice of the two leading terms. %C A308293 The variant, say b, with b(1) = b(2) = 1, corresponds to the natural numbers interspersed with pairs of ones: 1,1,1, 2,1,1, 3,1,1, etc. (b(n) = abs(A157128(n))). %H A308293 Rémy Sigrist, <a href="/A308293/b308293.txt">Table of n, a(n) for n = 1..10000</a> %H A308293 Rémy Sigrist, <a href="/A308293/a308293.png">Colored scatterplot of (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) for n = 1..32702782</a> (where the hue is function of n) %H A308293 Rémy Sigrist, <a href="/A308293/a308293.txt">C program for A308293</a> %e A308293 The first terms, alongside (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))), are: %e A308293 n a(n) (abs(a(n+2)-a(n)),abs(a(n+2)-a(n+1))) %e A308293 -- ---- ------------------------------------- %e A308293 1 1 (0,1) %e A308293 2 2 (1,0) %e A308293 3 1 (0,0) %e A308293 4 1 (1,1) %e A308293 5 1 (2,1) %e A308293 6 2 (1,2) %e A308293 7 3 (2,0) %e A308293 8 1 (2,2) %e A308293 9 1 (0,2) %e A308293 10 3 (1,3) %e A308293 11 1 (0,3) %e A308293 12 4 (3,0) %e A308293 13 1 (3,3) %e A308293 14 1 (4,1) %e A308293 15 4 (3,4) %o A308293 (C) See Links section. %Y A308293 See A080427 for a simpler variant. %Y A308293 Cf. A157128. %K A308293 nonn %O A308293 1,2 %A A308293 _Rémy Sigrist_, May 19 2019