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A334222 a(n) is the X-coordinate of the point at n steps backward from the origin along the space filling curve U defined in A334188; sequence A334223 gives Y-coordinates.

%I A334222 #13 May 06 2025 11:20:31
%S A334222 0,0,0,0,1,1,1,2,2,2,2,1,0,0,0,0,1,1,1,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,
%T A334222 5,6,6,6,6,5,4,4,4,3,3,3,2,1,0,0,0,0,1,1,1,2,2,2,2,1,0,0,0,0,1,1,1,2,
%U A334222 2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,6,6,6,7
%N A334222 a(n) is the X-coordinate of the point at n steps backward from the origin along the space filling curve U defined in A334188; sequence A334223 gives Y-coordinates.
%H A334222 Rémy Sigrist, <a href="/A334222/b334222.txt">Table of n, a(n) for n = 0..8318</a>
%H A334222 Rémy Sigrist, <a href="/A334222/a334222.gp.txt">PARI program for A334222</a>
%H A334222 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A334222 A334188(A334223(n), a(n)) = -n.
%e A334222 The "backward" branch of curve U starting from the origin is as follows:
%e A334222      |                                  |
%e A334222     7|  -15..-16  -21..-22  -31..-32  -37
%e A334222      |    |    |    |    |    |    |    |
%e A334222     6|  -14  -17  -20  -23  -30  -33  -36
%e A334222      |    |    |    |    |    |    |    |
%e A334222     5|  -13  -18..-19  -24  -29  -34..-35
%e A334222      |    |              |    |
%e A334222     4|  -12..-11..-10  -25  -28
%e A334222      |              |    |    |
%e A334222     3|   -3...-4   -9  -26..-27
%e A334222      |    |    |    |
%e A334222     2|   -2   -5   -8
%e A334222      |    |    |    |
%e A334222     1|   -1   -6...-7
%e A334222      |    |
%e A334222     0|    0
%e A334222   ---+-----------------------------------
%e A334222   y/x|    0    1    2    3    4    5    6
%e A334222 - hence a(4) = a(5) = a(6) = a(11) = a(16) = a(17) = a(18) = 1.
%o A334222 (PARI) See Links section.
%Y A334222 Cf. A334188, A334223.
%K A334222 nonn
%O A334222 0,8
%A A334222 _Rémy Sigrist_, Apr 19 2020