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%I #13 Nov 30 2020 22:37:57
%S 0,0,1,1,-2,-2,-1,-1,2,2,3,3,0,0,1,1,0,0,1,1,-2,-2,-1,-1,2,2,3,3,0,0,
%T 1,1,-4,-4,-3,-3,-6,-6,-5,-5,-2,-2,-1,-1,-4,-4,-3,-3,-4,-4,-3,-3,-6,
%U -6,-5,-5,-2,-2,-1,-1,-4,-4,-3,-3,8,8,9,9,6,6,7,7,10
%N For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the imaginary part of h(n).
%C See A318438 for the real part of h and additional comments.
%H Rémy Sigrist, <a href="/A318439/b318439.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(2^k) = A108520(k-1) for any k > 0.
%o (PARI) a(n) = my (d=Vecrev(digits(n,2))); imag(sum(i=1, #d, d[i]*(I-1)^(i-1)))
%Y Cf. A108520, A318438.
%K sign,look,base
%O 0,5
%A _Rémy Sigrist_, Aug 26 2018
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