This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305258 #34 Jul 30 2021 08:34:53 %S A305258 0,0,1,0,-1,-1,0,1,2,1,0,-1,-2,-2,-1,0,1,2,3,2,1,0,-1,-2,-3,-3,-2,-1, %T A305258 0,1,2,3,4,3,2,1,0,-1,-2,-3,-4,-4,-3,-2,-1,0,1,2,3,4,5,4,3,2,1,0,-1, %U A305258 -2,-3,-4,-5,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,5,4,3,2,1,0,-1,-2,-3 %N A305258 List of y-coordinates of a point moving in a smooth counterclockwise spiral rotated by Pi/4. %H A305258 Hugo Pfoertner, <a href="/A305258/a305258.png">Illustration of spiral</a>. %H A305258 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a> %F A305258 a(n) = A053616(n)*sign(sin(Pi*(1+sqrt(1+8*n))/2)), so that abs(a(n)) = A053616(n). %F A305258 a(n) = A010751(n-floor((1/2)*(sqrt(2n-1)+1))). - _William McCarty_, Jul 29 2021 %e A305258 Sequence gives y-coordinate of the n-th point of the following spiral: %e A305258 d: %e A305258 4 | 32 49 %e A305258 | / \ \ %e A305258 3 | 33 18 31 48 %e A305258 | / / \ \ \ %e A305258 2 | 34 19 8 17 30 47 %e A305258 | / / / \ \ \ \ %e A305258 1 | 35 20 9 2 7 16 29 46 %e A305258 | / / / / \ \ \ \ \ %e A305258 0 | 36 21 10 3 0---1 6 15 28 45 %e A305258 | \ \ \ \ / / / / %e A305258 -1 | 37 22 11 4---5 14 27 44 %e A305258 | \ \ \ / / / %e A305258 -2 | 38 23 12--13 26 43 %e A305258 | \ \ / / %e A305258 -3 | 39 24--25 42 %e A305258 | \ / %e A305258 -4 | 40--41 %e A305258 _______________________________________ %e A305258 x: -4 -3 -2 -1 0 1 2 3 4 5 %o A305258 (PARI) up=-1;print1(x=0,", ");for(stride=1,12,up=-up;x+=stride;y=x+stride+1;for(k=x,y-1,print1(up*min(k-x,y-k), ", "))) \\ _Hugo Pfoertner_, Jun 02 2018 %Y A305258 A010751 gives sequence of x-coordinates. %Y A305258 Cf. A053616. %Y A305258 Cf. A000384, A001105, A002024, A014105, A046092. %K A305258 sign %O A305258 0,9 %A A305258 _Hugo Pfoertner_, May 29 2018