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A332246
a(n) is the X-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332247 gives Y-coordinates.
4
0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 5, 5, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 8, 7, 7, 8, 8, 8, 9, 9, 8, 7, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 11, 11, 12, 13, 13, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 15, 15, 16, 17, 17, 16, 16, 15, 15, 14
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 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.
We can also build the curve by successively applying the following substitution to an initial vector (1, 0):
.--->.
^ |
| v
.--->. . .--->.
| ^
v |
.--->.
FORMULA
a(8^k-m) + a(m) = 4^k for any k >= 0 and m = 0..8^k.
PROG
(PARI) { dd = [0, 1, 0, -1, -1, 0, 1, 0]; z=0; for (n=0, 75, print1 (real(z)", "); z += I^vecsum(apply(d -> dd[1+d], digits(n, #dd)))) }
CROSSREFS
See A163528, A323258 and A332204 for similar sequences.
Cf. A332247 (Y-coordinates).
Sequence in context: A077105 A173752 A153847 * A096036 A108504 A036468
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 08 2020
STATUS
approved