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A340172 List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.

%I A340172 #16 Jan 03 2021 06:43:04
%S A340172 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 A340172 -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 A340172 5,5,5,5,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-6,-6,-6
%N A340172 List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.
%C A340172 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 A340172 Rémy Sigrist, <a href="/A340172/b340172.txt">Table of n, a(n) for n = 0..10000</a>
%H A340172 Rémy Sigrist, <a href="/A340172/a340172.gp.txt">PARI program for A340172</a>
%H A340172 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A340172 abs(a(n+1)-a(n)) + abs(A340171(n+1)-A340171(n)) = 1.
%F A340172 a(n) = A340171(n) iff n belongs to A001105.
%F A340172 a(n) = - A340171(n) iff n belongs to A046092.
%F A340172 2*a(n) = A340171(n) iff n belongs to A139274.
%F A340172 a(n) = 2*A340171(n) iff n belongs to A139275.
%F A340172 a(n) * A340171(n) = 0 iff n belongs to A000217.
%F A340172 a(n) = 0 iff n belongs to A000384.
%e A340172 The spiral starts as follows:
%e A340172       +-----+-----+-----+-----+-----+
%e A340172       .                             |
%e A340172       .                             |
%e A340172       .     +-----+-----+-----+     +
%e A340172       .     |5     4     3    |2    |
%e A340172       .     |                 |     |
%e A340172             +     +-----+-----+     +
%e A340172             |6    |      0     1    |     .
%e A340172             |     |                 |     .
%e A340172             +     +-----+-----+-----+     .
%e A340172             |7                            .
%e A340172             |                             .
%e A340172             +-----+-----+-----+-----+-----+
%e A340172              8     9     10    11    12    13
%e A340172 - so a(0) = a(1) = a(6) = 0,
%e A340172 -    a(2) = a(3) = a(4) = a(5) = 1.
%o A340172 (PARI) See Links section.
%Y A340172 Cf. A000217, A000384, A001105, A046092, A139274, A139275, A274923, A340171.
%K A340172 sign
%O A340172 0,9
%A A340172 _Rémy Sigrist_, Dec 30 2020