A308081 Index positions of the points of a counterclockwise square spiral as described by A174344 and A274923 in a list of points with integer coordinates with primary sorting by radius and secondary sorting by polar angle as given by A305575 and A305576.

0, 1, 5, 2, 6, 3, 7, 4, 8, 20, 9, 13, 21, 14, 10, 15, 22, 16, 11, 17, 23, 18, 12, 19, 24, 44, 36, 25, 29, 37, 57, 38, 30, 26, 31, 39, 58, 40, 32, 27, 33, 41, 59, 42, 34, 28, 35, 43, 60, 80, 68, 56, 45, 49, 61, 70, 97, 71, 62, 50, 46, 51, 63, 73, 98, 74, 64

Offset: 1

Author

Hugo Pfoertner, May 11 2019

Keywords

• nonn

Comments

The sequence is a permutation of the integers.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A174344, A274923, A305575, A305576, A308080.

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));
findinring(i, j)={my(s=i*i+j*j);if(s==0,return(0),forstep(k=floor(Pi*(s+1))+sqrtint(s),1,-1,if(i==a305575[k]&&j==a305576[k], return(k))))};
for(n=1,67,print1(findinring(a174344[n],a274923[n]),", "));