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 A059253 #22 Jun 08 2021 13:54:29 %S A059253 0,1,1,0,0,0,1,1,2,2,3,3,3,2,2,3,4,4,5,5,6,7,7,6,6,7,7,6,5,5,4,4,4,4, %T A059253 5,5,6,7,7,6,6,7,7,6,5,5,4,4,3,2,2,3,3,3,2,2,1,1,0,0,0,1,1,0,0,0,1,1, %U A059253 2,3,3,2,2,3,3,2,1,1,0,0,0,1,1,0,0,0,1,1,2,2,3,3,3,2,2,3,4,5,5,4,4,4 %N A059253 Hilbert's Hamiltonian walk on N X N projected onto y axis: m'(3). %C A059253 This is the Y-coordinate of the n-th term in the type I Hilbert's Hamiltonian walk A163359 and the X-coordinate of its transpose A163357. %H A059253 Antti Karttunen, <a href="/A059253/b059253.txt">Table of n, a(n) for n = 0..65535</a> %H A059253 J. Shallit, <a href="https://arxiv.org/abs/2106.01062">Hilbert's spacefilling curve described by automatic, regular, and synchronized sequences</a>, arXiv:2106.01062 [cs.FL], June 2 2021. %H A059253 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a> %F A059253 Initially [m(0) = 0, m'(0) = 0]; recursion: m(2n + 1) = m(2n).m'(2n).f(m'(2n), 2n).c(m(2n), 2n + 1); m'(2n + 1) = m'(2n).f(m(2n), 2n).f(m(2n), 2n).mir(m'(2n)); m(2n) = m(2n - 1).f(m'(2n - 1), 2n - 1).f(m'(2n - 1), 2n - 1).mir(m(2n - 1)); m'(2n) = m'(2n - 1).m(2n - 1).f(m(2n - 1), 2n - 1).c(m'(2n - 1), 2n); where f(m, n) is the alphabetic morphism i := i + 2^n [example: f(0 0 1 1 2 3 3 2 2 3 3 2 1 1 0 0, 2) = 4 4 5 5 6 7 7 6 6 7 7 6 5 5 4 4]; c(m, n) is the complementation to 2^n - 1 alphabetic morphism [example: c(0 0 1 1 2 3 3 2 2 3 3 2 1 1 0 0, 3) = 7 7 6 6 5 4 4 5 5 4 4 5 6 6 7 7]; and mir(m) is the mirror operator [example: mir(0 1 1 0 0 0 1 1 2 2 3 3 3 2 2 3) = 3 2 2 3 3 3 2 2 1 1 0 0 0 1 1 0]. %F A059253 a(n) = A025581(A163358(n)) = A002262(A163360(n)) = A059905(A163356(n)). %o A059253 (C) See A059252. %Y A059253 See also the y-projection, m(3), A059252 as well as A163538, A163540, A163542, A059261, A059285, A163547 and A163528. %K A059253 nonn %O A059253 0,9 %A A059253 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 23 2001 %E A059253 Extended by _Antti Karttunen_, Aug 01 2009