A308080 Index positions of the points with integer coordinates with primary sorting by radius and secondary sorting by polar angle in the counterclockwise square spiral described by A174344 and A274923.

1, 2, 4, 6, 8, 3, 5, 7, 9, 11, 15, 19, 23, 12, 14, 16, 18, 20, 22, 24, 10, 13, 17, 21, 25, 28, 34, 40, 46, 29, 33, 35, 39, 41, 45, 47, 27, 30, 32, 36, 38, 42, 44, 48, 26, 53, 61, 69, 77, 54, 60, 62, 68, 70, 76, 78, 52, 31, 37, 43, 49, 55, 59, 63, 67, 71, 75, 79

Offset

0,2

Comments

The lists of the ring-wise sorted points is provided in A305575 for x and A305576 for y.

The sequence is a permutation of the integers.

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..10000

Prog

(PARI) /* It is assumed that the files a305575 and a305576 contain the second column of the corresponding b-files omitting the initial 0 */
a305575=readvec(a305575); a305576=readvec(a305576);
a174344=vector(10000); L=0; d=1; n=0;
for(r=1, 100, d=-d; k=floor(r/2)*d; for(j=1, L++, a174344[n++]=k); forstep(j=k-d, -floor((r+1)/2)*d+d, -d, a174344[n++]=j));
a274923=vector(10100); L=1; d=1; n=0;
for(r=1, 100, d=-d; k=floor(r/2)*d; for(j=1, L++, a274923[n++]=k); forstep(j=k-d, -floor((r+1)/2)*d+d, -d, a274923[n++]=j));
findinspiral(i, j)={my(size=(2*max(abs(i), abs(j))+1)^2); forstep(k=size, 1, -1, if(i==a174344[k]&&j==a274923[k], return(k)))};
print1(findinspiral(0, 0), ", "); for(n=1, 67, print1(findinspiral(a305575[n], a305576[n]), ", "));

Crossrefs

Cf. A174344, A274923, A305575, A305576, A308081.

Sequence in context: A106202 A351330 A220102 * A179657 A239887 A354721

Adjacent sequences: A308077 A308078 A308079 * A308081 A308082 A308083

Keyword

nonn

Author

Hugo Pfoertner, May 11 2019

Status

approved