A332205 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).

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

Offset

0,7

Comments

Looks much like A005536, in particular in respect of its symmetries of scale (compare the scatterplots). - Peter Munn, Jun 21 2021

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Larry Riddle, Koch Curve

Rémy Sigrist, PARI program for A332205

Index entries for sequences related to coordinates of 2D curves

Formula

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

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

Mathematica

A065359[0] = 0;
A065359[n_] := -Total[(-1)^PositionIndex[Reverse[IntegerDigits[n, 2]]][1]];
g[z_] := z/GCD[Re[z], Im[z]];
Module[{n = 0}, Im[NestList[# + g[(1+I)^A065359[n++]] &, 0, 100]]] (* Paolo Xausa, Aug 28 2024 *)

Prog

(PARI) \\ See Links section.

Crossrefs

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

Sequence in context: A318958 A194827 A335359 * A219237 A138774 A156988

Adjacent sequences: A332202 A332203 A332204 * A332206 A332207 A332208

Keyword

nonn,look,base

Author

Rémy Sigrist, Feb 07 2020

Status

approved