cp's OEIS Frontend

A362955 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 distance-limited strip bijection described in A307110.

%I A362955 #19 Aug 24 2025 05:51:59
%S A362955 0,1,0,-1,-2,-1,0,1,2,2,1,1,0,0,-1,-2,-3,-2,-1,-1,0,0,1,2,3,4,3,2,2,1,
%T A362955 0,-1,-1,-2,-3,-3,-4,-4,-3,-2,-2,-1,0,1,1,2,3,3,4,5,4,3,3,2,1,0,0,-1,
%U A362955 -2,-2,-3,-4,-4,-5,-5,-5,-4,-3,-3,-2,-1,0,0,1,2,2,3,4,4,5,5,6
%N A362955 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 distance-limited strip bijection described in A307110.
%H A362955 Hugo Pfoertner, <a href="/A362955/b362955.txt">Table of n, a(n) for n = 0..3000</a>
%H A362955 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A362955&amp;name2=A362956&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=xy&amp;drawlines=true">Plot of mapped spiral</a>, using Plot 2.
%o A362955 (PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923,
%o A362955 \\ p(i,j) given in A307110
%o A362955 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 A362955 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 A362955 p(i, j) = {my(C=cos(Pi/8), S=sin(Pi/8), T=S/C, gx=i*C-j*S, gy=i*S+j*C, k, xm, ym, v=[0, 0]); k=round(gy/C); ym=C*k; xm=gx+(gy-ym)*T; v[1]=round((xm-ym*T)*C);  v[2]=round((ym+v[1]*S)/C);  v};
%o A362955 for (k=0, 81, print1 (p(ax(k),ay(k))[1]", "))
%Y A362955 A362956 gives the corresponding y-coordinates.
%Y A362955 Cf. A174344, A274923, A307110, A307731, A367150, A367895, A367896.
%K A362955 sign,changed
%O A362955 0,5
%A A362955 _Hugo Pfoertner_, May 10 2023