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.

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, 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, -2, -2, -3, -4, -4, -5, -5, -5, -4, -3, -3, -2, -1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 6

Offset

0,5

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..3000

Hugo Pfoertner, Plot of mapped spiral, using Plot 2.

Prog

(PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923,
\\ p(i, j) given in A307110
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))};
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))};
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};
for (k=0, 81, print1 (p(ax(k), ay(k))[1]", "))

Crossrefs

A362956 gives the corresponding y-coordinates.

Cf. A174344, A274923, A307110, A307731.

Sequence in context: A365746 A094718 A076191 * A282318 A286971 A025861

Adjacent sequences: A362952 A362953 A362954 * A362956 A362957 A362958

Keyword

sign

Author

Hugo Pfoertner, May 10 2023

Status

approved