A332381 a(n) is the Y-coordinate of the n-th point of the Peano curve. Sequence A332380 gives X-coordinates.

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

Offset: 0

Author

Rémy Sigrist, Feb 10 2020

Keywords

• sign
• 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 7's minus the number of 3's and 5's

plus twice the number of 4's in the base 9 representation of n

and i denotes the imaginary unit.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A332380 (X-coordinates and additional comments).

Programs

PARI

{ [R,U,L,D]=[0..3]; p = [R,U,R,D,L,D,R,U,R]; z=0; for (n=0, 76, print1 (imag(z) ", "); z += I^vecsum(apply(d -> p[1+d], digits(n, #p)))) }

Formula

a(9^k) = 0 for any k >= 0.