A332205 - OEIS

%I #35 Aug 30 2024 10:18:47

%S 0,0,1,0,0,1,2,2,3,2,2,1,0,0,1,0,0,1,2,2,3,4,5,6,7,7,8,7,7,8,9,9,10,9,

%T 9,8,7,7,8,7,7,6,5,4,3,2,2,1,0,0,1,0,0,1,2,2,3,2,2,1,0,0,1,0,0,1,2,2,

%U 3,4,5,6,7,7,8,7,7,8,9,9,10,11,12,13,14

%N a(n) is the imaginary part of f(n) defined by f(0) = 0, and f(n+1) = f(n) + g((1+i)^(A065359(n) mod 8)) (where g(z) = z/gcd(Re(z), Im(z)) and i denotes the imaginary unit).

%C Looks much like A005536, in particular in respect of its symmetries of scale (compare the scatterplots). - _Peter Munn_, Jun 21 2021

%H Rémy Sigrist, <a href="/A332205/b332205.txt">Table of n, a(n) for n = 0..16384</a>

%H Larry Riddle, <a href="http://ecademy.agnesscott.edu/~lriddle/ifs/kcurve/kcurve.htm">Koch Curve</a>

%H Rémy Sigrist, <a href="/A332205/a332205.gp.txt">PARI program for A332205</a>

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

%F a(2^(2*k-1)) = A007052(k) for any k >= 0.

%F a(4^k-m) = a(m) for any k >= 0 and m = 0..4^k.

%t A065359[0] = 0;

%t A065359[n_] := -Total[(-1)^PositionIndex[Reverse[IntegerDigits[n, 2]]][1]];

%t g[z_] := z/GCD[Re[z], Im[z]];

%t Module[{n = 0}, Im[NestList[# + g[(1+I)^A065359[n++]] &, 0, 100]]] (* _Paolo Xausa_, Aug 28 2024 *)

%o (PARI) \\ See Links section.

%Y Cf. A005536, A007052, A065359, A332204 (real part and additional comments), A332206 (positions of 0's, cf. A001196).

%K nonn,look,base

%O 0,7

%A _Rémy Sigrist_, Feb 07 2020