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A332252 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.

%I A332252 #18 Dec 20 2024 03:54:57
%S A332252 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 A332252 -5,-5,-4,-3,-3,-3,-4,-4,-5,-6,-6,-6,-7,-8,-8,-9,-9,-9,-8,-8,-9,-10,
%U A332252 -10,-11,-11,-11,-10,-11,-11,-11,-10,-10,-9,-8,-8,-7,-7,-7
%N A332252 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 A332252 Rémy Sigrist, <a href="/A332252/b332252.txt">Table of n, a(n) for n = 0..8192</a>
%H A332252 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A332252 For any k >= 0:
%F A332252 - a(2^(4*k))   =        0,
%F A332252 - a(2^(4*k+1)) =   (-4)^k,
%F A332252 - a(2^(4*k+2)) = 2*(-4)^k,
%F A332252 - a(2^(4*k+3)) = 2*(-4)^k.
%o A332252 (PARI) { z=0; for (n=0, 67, print1 (imag(z) ", "); z += I^hammingweight(n)) }
%Y A332252 Cf. A000120, A332251 (real parts and additional comments).
%K A332252 sign,base
%O A332252 0,4
%A A332252 _Rémy Sigrist_, Feb 08 2020