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%I #15 Feb 12 2020 16:18:53
%S 0,0,1,1,0,0,-1,-1,0,0,1,1,2,2,1,1,2,2,3,3,4,4,3,3,2,2,3,3,2,2,1,1,2,
%T 2,1,1,0,0,-1,-1,0,0,1,1,0,0,-1,-1,-2,-2,-1,-1,-2,-2,-3,-3,-2,-2,-3,
%U -3,-4,-4,-3,-3,-2,-2,-1,-1,-2,-2,-1,-1,0,0,1,1,0
%N a(n) is the Y-coordinate of the n-th point of the Peano curve. Sequence A332380 gives X-coordinates.
%C This sequence is the imaginary part of {f(n)} defined as:
%C - f(0) = 0,
%C - f(n+1) = f(n) + i^t(n)
%C where t(n) is the number of 1's and 7's minus the number of 3's and 5's
%C plus twice the number of 4's in the base 9 representation of n
%C and i denotes the imaginary unit.
%H Rémy Sigrist, <a href="/A332381/b332381.txt">Table of n, a(n) for n = 0..6561</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F a(9^k) = 0 for any k >= 0.
%o (PARI) { [R,U,L,D]=[0..3]; p = [R,U,R,D,L,D,R,U,R]; z=0; for (n=0, 76, print1 (imag(z) ", "); z += I^vecsum(apply(d -> p[1+d], digits(n, #p)))) }
%Y Cf. A332380 (X-coordinates and additional comments).
%K sign,base
%O 0,13
%A _Rémy Sigrist_, Feb 10 2020
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