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

Author

Hugo Pfoertner, May 11 2019

Keywords

• nonn

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

Crossrefs

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

Programs

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]),", "));