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

1,3

Comments

The sequence is a permutation of the integers.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..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));
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]), ", "));

Crossrefs

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

Sequence in context: A021099 A021023 A078716 * A164103 A054863 A257812

Adjacent sequences: A308078 A308079 A308080 * A308082 A308083 A308084

Keyword

nonn

Author

Hugo Pfoertner, May 11 2019

Status

approved