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

%I A340171 #17 Jan 03 2021 06:43:10
%S A340171 0,1,1,0,-1,-2,-2,-2,-2,-1,0,1,2,3,3,3,3,3,3,2,1,0,-1,-2,-3,-4,-4,-4,
%T A340171 -4,-4,-4,-4,-4,-3,-2,-1,0,1,2,3,4,5,5,5,5,5,5,5,5,5,5,4,3,2,1,0,-1,
%U A340171 -2,-3,-4,-5,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-5
%N A340171 List of X-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340172 gives Y-coordinates.
%C A340171 The odd function f such that f(n) = (a(n), A340172(n)) for any n >= 0 will visit exactly once every lattice point (so it is a bijection from Z to Z^2).
%H A340171 Rémy Sigrist, <a href="/A340171/b340171.txt">Table of n, a(n) for n = 0..10000</a>
%H A340171 Rémy Sigrist, <a href="/A340171/a340171.gp.txt">PARI program for A340171</a>
%H A340171 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A340171 abs(a(n+1)-a(n)) + abs(A340172(n+1)-A340172(n)) = 1.
%F A340171 a(n) = A340172(n) iff n belongs to A001105.
%F A340171 a(n) = -A340172(n) iff n belongs to A046092.
%F A340171 a(n) = 2*A340172(n) iff n belongs to A139274.
%F A340171 2*a(n) = A340172(n) iff n belongs to A139275.
%F A340171 a(n) * A340172(n) = 0 iff n belongs to A000217.
%F A340171 a(n) = 0 iff n belongs to A014105.
%e A340171 The spiral starts as follows:
%e A340171       +-----+-----+-----+-----+-----+
%e A340171       .                             |
%e A340171       .                             |
%e A340171       .     +-----+-----+-----+     +
%e A340171       .     |5     4     3    |2    |
%e A340171       .     |                 |     |
%e A340171             +     +-----+-----+     +
%e A340171             |6    |      0     1    |     .
%e A340171             |     |                 |     .
%e A340171             +     +-----+-----+-----+     .
%e A340171             |7                            .
%e A340171             |                             .
%e A340171             +-----+-----+-----+-----+-----+
%e A340171              8     9     10    11    12    13
%e A340171 - so a(0) = a(3) = a(10) = 0,
%e A340171 -    a(1) = a(2) = a(11) = 1.
%o A340171 (PARI) See Links section.
%Y A340171 Cf. A000217, A014105, A046092, A001105, A139274, A139275, A174344, A340172.
%K A340171 sign
%O A340171 0,6
%A A340171 _Rémy Sigrist_, Dec 30 2020