A332247 a(n) is the Y-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332246 gives X-coordinates.

0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 4, 3, 3, 4, 4, 3, 3, 2, 2, 2, 1, 1, 0, -1, -1, -2, -2, -2, -3, -3, -4, -4, -3, -3, -4, -5, -5, -4, -4, -3, -3, -2, -2, -2, -1, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 5

Offset: 0

Author

Rémy Sigrist, Feb 08 2020

Keywords

• sign
• look
• base

Comments

This sequence is the imaginary part of {f(n)} defined as:

- f(0) = 0,

- f(n+1) = f(n) + i^t(n)

where t(n) is the number of 1's and 6's minus the number of 3's and 4's

in the base 8 representation of n

and i denotes the imaginary unit.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..4096
• Robert Ferréol (MathCurve), Saucisse de Minkowski [in French]
• Wikipedia, Minkowski sausage
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A332246 (X-coordinates and additional comments).

Programs

PARI

{ dd = [0,1,0,-1,-1,0,1,0]; z=0; for (n=0, 77, print1 (imag(z)", "); z += I^vecsum(apply(d -> dd[1+d], digits(n, #dd)))) }

Formula

a(8^k-m) = -a(m) for any k >= 0 and m = 0..8^k.