A368127 - OEIS

%I #14 Jan 07 2024 14:07:27

%S 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 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 -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 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 Hugo Pfoertner, <a href="/A368127/b368127.txt">Table of n, a(n) for n = 0..3000</a>

%H 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 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%o (PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923.

%o \\ It is assumed that the PARI programs from A367150 and A368126 have been loaded and the functions defined there are available.

%o 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 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(n) = BijectionD([ax(n), ay(n)], Bijectionk)[1];

%Y A368128 gives the corresponding y-coordinates.

%Y Cf. A367150, A368126.

%Y Analogous sequences, but without symmetrization: A367895, A367896.

%K sign

%O 0,10

%A _Hugo Pfoertner_, Jan 07 2024