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

%I A334223 #13 May 06 2025 11:20:42
%S A334223 0,1,2,3,3,2,1,1,2,3,4,4,4,5,6,7,7,6,5,5,6,7,7,6,5,4,3,3,4,5,6,7,7,6,
%T A334223 5,5,6,7,8,8,8,9,10,10,9,8,8,8,8,9,10,11,11,10,9,9,10,11,12,12,12,13,
%U A334223 14,15,15,14,13,13,14,15,15,14,13,12,11,11,12,13
%N A334223 a(n) is the Y-coordinate of the point at n steps backward from the origin along the space filling curve U defined in A334188; sequence A334222 gives X-coordinates.
%H A334223 Rémy Sigrist, <a href="/A334223/b334223.txt">Table of n, a(n) for n = 0..8318</a>
%H A334223 Rémy Sigrist, <a href="/A334223/a334223.gp.txt">PARI program for A334223</a>
%H A334223 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A334223 A334188(a(n), A334223(n)) = -n.
%e A334223 The "backward" branch of curve U starting from the origin is as follows:
%e A334223      |                                  |
%e A334223     7|  -15..-16  -21..-22  -31..-32  -37
%e A334223      |    |    |    |    |    |    |    |
%e A334223     6|  -14  -17  -20  -23  -30  -33  -36
%e A334223      |    |    |    |    |    |    |    |
%e A334223     5|  -13  -18..-19  -24  -29  -34..-35
%e A334223      |    |              |    |
%e A334223     4|  -12..-11..-10  -25  -28
%e A334223      |              |    |    |
%e A334223     3|   -3...-4   -9  -26..-27
%e A334223      |    |    |    |
%e A334223     2|   -2   -5   -8
%e A334223      |    |    |    |
%e A334223     1|   -1   -6...-7
%e A334223      |    |
%e A334223     0|    0
%e A334223   ---+-----------------------------------
%e A334223   y/x|    0    1    2    3    4    5    6
%e A334223 - hence a(10) = a(11) = a(12) = a(25) = a(28) = 4.
%o A334223 (PARI) See Links section.
%Y A334223 Cf. A334188, A334222.
%K A334223 nonn
%O A334223 0,3
%A A334223 _Rémy Sigrist_, Apr 19 2020