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A368127 a(n) is the x-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the symmetrized variant of the distance-limited strip bijection described in A368126.

%I A368127 #14 Jan 07 2024 14:07:27
%S A368127 0,1,0,-1,-1,-1,0,1,1,2,2,1,0,0,-1,-2,-3,-2,-2,-1,0,0,1,2,3,3,3,2,2,1,
%T A368127 0,-1,-2,-2,-3,-3,-4,-3,-3,-2,-2,-1,0,1,2,2,3,3,4,5,4,4,3,2,1,0,0,-1,
%U A368127 -1,-2,-3,-4,-4,-5,-6,-5,-4,-4,-3,-2,-1,0,0,1,1,2,3,4,4,5,6,6,6,5,4,3
%N A368127 a(n) is the x-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the symmetrized variant of the distance-limited strip bijection described in A368126.
%H A368127 Hugo Pfoertner, <a href="/A368127/b368127.txt">Table of n, a(n) for n = 0..3000</a>
%H A368127 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A368127&amp;name2=A368128&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=xy&amp;drawlines=true">Plot of mapped spiral</a>, using Plot 2.
%H A368127 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%o A368127 (PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923.
%o A368127 \\ It is assumed that the PARI programs from A367150 and A368126 have been loaded and the functions defined there are available.
%o A368127 ax(n) = {my (m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if (n<0, if (n<-m, k, -k-n), if (n<m, -k, n-3*k))};
%o A368127 ay(n) = {my (m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if (n<0, if (n<-m, 3*k+n, k), if (n<m, k-n, -k))};
%o A368127 a368127(n) = BijectionD([ax(n), ay(n)], Bijectionk)[1];
%Y A368127 A368128 gives the corresponding y-coordinates.
%Y A368127 Cf. A367150, A368126.
%Y A368127 Analogous sequences, but without symmetrization: A367895, A367896.
%K A368127 sign
%O A368127 0,10
%A A368127 _Hugo Pfoertner_, Jan 07 2024