This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348761 #10 Nov 01 2021 13:46:04
%S A348761 0,0,1,-1,2,-2,-1,1,2,-2,-1,1,0,0,1,-1,0,0,1,-1,2,-2,-1,1,2,-2,-1,1,0,
%T A348761 0,1,-1,-4,4,5,-5,6,-6,-5,5,6,-6,-5,5,-4,4,5,-5,4,-4,-3,3,-2,2,3,-3,
%U A348761 -2,2,3,-3,4,-4,-3,3,-8,8,9,-9,10,-10,-9,9,10,-10
%N A348761 For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the imaginary part of f(n) = Sum_{k >= 0} ((-1)^Sum_{j = 0..k-1} b_j) * (1+i)^k (where i denotes the imaginary unit); sequence A348760 gives the real part.
%C A348761 The function f defines a bijection from the nonnegative integers to the Gaussian integers.
%H A348761 Rémy Sigrist, <a href="/A348761/b348761.txt">Table of n, a(n) for n = 0..8191</a>
%H A348761 Rémy Sigrist, <a href="/A348760/a348760.png">Colored representation of f(n) for n < 2^20 in the complex plane</a> (the hue is function of n)
%H A348761 Rémy Sigrist, <a href="/A348760/a348760_1.png">Colored representation of f(n) for n < 2^18 in the complex plane</a> (the color is function of A000120(n) mod 2)
%H A348761 Rémy Sigrist, <a href="/A348760/a348760_2.png">Colored representation of f(n) for n < 2^18 in the complex plane</a> (the color is function of the binary length of n, A070939(n))
%H A348761 Rémy Sigrist, <a href="/A348760/a348760_3.png">Colored representation of f(n) for n < 2^18 in the complex plane</a> (the color is function of A000120(n), darker shades correspond to higher values)
%F A348761 a(2^k) = A009545(k) for any k >= 0.
%o A348761 (PARI) a(n) = { my (v=0, k, o=-1); while (n, n-=2^k=valuation(n,2); v+=(1+I)^k * (-1)^o++); imag(v) }
%Y A348761 See A348691 for a similar sequence.
%Y A348761 Cf. A000120, A009545, A070939, A348760.
%K A348761 sign,look,base
%O A348761 0,5
%A A348761 _Rémy Sigrist_, Oct 31 2021