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%I #9 May 16 2019 21:49:16
%S 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,
%T 34,40,46,29,33,35,39,41,45,47,27,30,32,36,38,42,44,48,26,53,61,69,77,
%U 54,60,62,68,70,76,78,52,31,37,43,49,55,59,63,67,71,75,79
%N 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.
%C The lists of the ring-wise sorted points is provided in A305575 for x and A305576 for y.
%C The sequence is a permutation of the integers.
%H Hugo Pfoertner, <a href="/A308080/b308080.txt">Table of n, a(n) for n = 0..10000</a>
%o (PARI) /* It is assumed that the files a305575 and a305576 contain the second column of the corresponding b-files omitting the initial 0 */
%o a305575=readvec(a305575); a305576=readvec(a305576);
%o a174344=vector(10000);L=0; d=1; n=0;
%o 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));
%o a274923=vector(10100);L=1; d=1;n=0;
%o 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));
%o 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)))};
%o print1(findinspiral(0,0),", ");for(n=1,67,print1(findinspiral(a305575[n],a305576[n]),", "));
%Y Cf. A174344, A274923, A305575, A305576, A308081.
%K nonn
%O 0,2
%A _Hugo Pfoertner_, May 11 2019
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