A332250 a(n) is the Y-coordinate of the n-th point of the quadratic Koch curve. Sequence A332249 gives X-coordinates.

0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 10, 10, 9, 9, 8, 8, 7, 7, 6

Offset: 0

Author

Rémy Sigrist, Feb 08 2020

Keywords

• nonn
• 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 minus the number of 3's

in the base 5 representation of n

and i denotes the imaginary unit.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..15625
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A332249 (X-coordinates and additional comments).

Programs

PARI

{ k = [0, 1, 0, -1, 0]; z=0; for (n=0, 80, print1 (imag(z) ", "); z += I^vecsum(apply(d -> k[1+d], digits(n, #k)))) }

Formula

a(5^k-m) = a(m) for any k >= 0 and m = 0..5^k.