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 A138684 #11 Sep 11 2021 17:58:07 %S A138684 1,3,1,1,4,1,3,1,1,1,1,6,1,3,1,1,4,1,3,1,1,1,1,1,1,1,1,1,11,1,3,1,1,4, %T A138684 1,3,1,1,1,1,6,1,3,1,1,4,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %U A138684 1,23,1,3,1,1,4,1,3,1,1,1,1,6,1,3,1,1,4,1,3,1,1,1,1,1,1,1,1,1,11,1,3,1,1,4,1 %N A138684 First differences of A138683. %C A138684 The graph of this sequence is fractal-like. %C A138684 Conjecture. Let x(1)=1, x(2)=2, x(n) = 2*x(n-1) + x(n-2), and let y(1)=1, y(2)=3, y(n) = y(n-1) + y(n-2). Then if n=x(k), a(n)=y(k); if x(k) < n < 2*x(k), a(n) = a(n-x(k)); and if 2*x(k) <= n < x(k+1), a(n)=1. (This has been confirmed for n < 500.) - _John W. Layman_, Nov 26 2011 %Y A138684 Cf. A114889, A114890, A138683. %K A138684 nonn %O A138684 1,2 %A A138684 _John W. Layman_, Mar 26 2008