OFFSET
0,4
COMMENTS
This sequence is the real 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.
We can also build the curve by successively applying the following substitution to an initial vector (1, 0):
.--->.
^ |
| v
.--->. .--->.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..15625
Robert Ferréol (MathCurve), Courbe de Koch quadratique [in French]
FORMULA
a(5^k-m) + a(m) = 3^k for any k >= 0 and m = 0..5^k.
PROG
(PARI) { k = [0, 1, 0, -1, 0]; z=0; for (n=0, 77, print1 (real(z) ", "); z += I^vecsum(apply(d -> k[1+d], digits(n, #k)))) }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 08 2020
STATUS
approved