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A332247
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a(n) is the Y-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332246 gives X-coordinates.
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2
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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
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,12
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COMMENTS
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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.
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LINKS
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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
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FORMULA
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a(8^k-m) = -a(m) for any k >= 0 and m = 0..8^k.
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PROG
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(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)))) }
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CROSSREFS
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Cf. A332246 (X-coordinates and additional comments).
Sequence in context: A025778 A294622 A078451 * A341168 A071824 A224921
Adjacent sequences: A332244 A332245 A332246 * A332248 A332249 A332250
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KEYWORD
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sign,look,base
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AUTHOR
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Rémy Sigrist, Feb 08 2020
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STATUS
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approved
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