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a(n) is the imaginary part of f(n) defined by f(0) = 0 and f(n+1) = f(n) + i^A000120(n) (where i denotes the imaginary unit). Sequence A332251 gives real parts.
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%I #14 Feb 12 2020 16:18:27

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

%T -5,-5,-4,-3,-3,-3,-4,-4,-5,-6,-6,-6,-7,-8,-8,-9,-9,-9,-8,-8,-9,-10,

%U -10,-11,-11,-11,-10,-11,-11,-11,-10,-10,-9,-8,-8,-7,-7,-7

%N a(n) is the imaginary part of f(n) defined by f(0) = 0 and f(n+1) = f(n) + i^A000120(n) (where i denotes the imaginary unit). Sequence A332251 gives real parts.

%H Rémy Sigrist, <a href="/A332252/b332252.txt">Table of n, a(n) for n = 0..8192</a>

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

%F For any k >= 0:

%F - a(2^(4*k)) = 0,

%F - a(2^(4*k+1)) = (-4)^k,

%F - a(2^(4*k+2)) = 2*(-4)^k,

%F - a(2^(4*k+3)) = 2*(-4)^k).

%o (PARI) { z=0; for (n=0, 67, print1 (imag(z) ", "); z += I^hammingweight(n)) }

%Y Cf. A000120, A332251 (real parts and additional comments).

%K sign,base

%O 0,4

%A _Rémy Sigrist_, Feb 08 2020