|
%I #17 Feb 09 2021 11:00:50
%S 0,1,0,1,1,1,2,1,2,1,0,1,0,1,1,1,2,1,2,2,2,2,2,3,2,3,3,3,4,3,4,3,2,3,
%T 2,3,3,3,4,3,4,3,2,1,0,1,0,1,1,1,2,1,2,1,0,1,0,1,1,1,2,1,2,2,2,2,2,3,
%U 2,3,3,3,4,3,4,3,2,3,2,3,3,3,4,3,4,4,4
%N a(n) is the X-coordinate of the n-th point of the space filling curve H defined in Comments section; A339456 gives Y-coordinates.
%C We consider a hexagonal lattice with X-axis and Y-axis as follows:
%C Y
%C /
%C /
%C 0 ---- X
%C We define the family {H_n, n > 0} as follows:
%C - T_1 contains the origin (0, 0) and (1, 0), in that order:
%C +-->--+
%C O
%C - for any n > 0, H_{n+1} is built from 4 copies of H_n connected with 2^(n+1) unit segments as follows:
%C +->-2->-+
%C \ /
%C ^ v
%C \ /
%C +->-1->-+->-4->-+
%C O / \
%C v ^
%C / \
%C +->-3->-+
%C - H is the limit of H_n as n tends to infinity,
%C - H visits once every unit segment (u, v) where u and v are lattice points and at least one of u or v belongs to the region { (x, y) | x > 0 or x + y > 0 },
%C - the n-th segment of curve H has length 2^A235127(n).
%H Rémy Sigrist, <a href="/A339455/b339455.txt">Table of n, a(n) for n = 0..3008</a>
%H Rémy Sigrist, <a href="/A339455/a339455.png">Illustration of H_3</a>
%H Rémy Sigrist, <a href="/A339455/a339455.gp.txt">PARI program for A339455</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%o (PARI) See Links section.
%Y Cf. A235127, A339456.
%K nonn
%O 0,7
%A _Rémy Sigrist_, Dec 06 2020
|
