%I #16 Jan 03 2021 06:43:04

%S 0,0,1,1,1,1,0,-1,-2,-2,-2,-2,-2,-2,-1,0,1,2,3,3,3,3,3,3,3,3,2,1,0,-1,

%T -2,-3,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-3,-2,-1,0,1,2,3,4,5,5,5,5,5,5,5,

%U 5,5,5,5,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-6,-6,-6

%N List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.

%C The odd function f such that f(n) = (A340171(n), a(n)) for any n >= 0 will visit exactly once every lattice point (so it is a bijection from Z to Z^2).

%H Rémy Sigrist, <a href="/A340172/b340172.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A340172/a340172.gp.txt">PARI program for A340172</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%F abs(a(n+1)-a(n)) + abs(A340171(n+1)-A340171(n)) = 1.

%F a(n) = A340171(n) iff n belongs to A001105.

%F a(n) = - A340171(n) iff n belongs to A046092.

%F 2*a(n) = A340171(n) iff n belongs to A139274.

%F a(n) = 2*A340171(n) iff n belongs to A139275.

%F a(n) * A340171(n) = 0 iff n belongs to A000217.

%F a(n) = 0 iff n belongs to A000384.

%e The spiral starts as follows:

%e +-----+-----+-----+-----+-----+

%e . |

%e . |

%e . +-----+-----+-----+ +

%e . |5 4 3 |2 |

%e . | | |

%e + +-----+-----+ +

%e |6 | 0 1 | .

%e | | | .

%e + +-----+-----+-----+ .

%e |7 .

%e | .

%e +-----+-----+-----+-----+-----+

%e 8 9 10 11 12 13

%e - so a(0) = a(1) = a(6) = 0,

%e - a(2) = a(3) = a(4) = a(5) = 1.

%o (PARI) See Links section.

%Y Cf. A000217, A000384, A001105, A046092, A139274, A139275, A274923, A340171.

%K sign

%O 0,9

%A _Rémy Sigrist_, Dec 30 2020