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A340171
List of X-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340172 gives Y-coordinates.
3
0, 1, 1, 0, -1, -2, -2, -2, -2, -1, 0, 1, 2, 3, 3, 3, 3, 3, 3, 2, 1, 0, -1, -2, -3, -4, -4, -4, -4, -4, -4, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -5
OFFSET
0,6
COMMENTS
The odd function f such that f(n) = (a(n), A340172(n)) for any n >= 0 will visit exactly once every lattice point (so it is a bijection from Z to Z^2).
FORMULA
abs(a(n+1)-a(n)) + abs(A340172(n+1)-A340172(n)) = 1.
a(n) = A340172(n) iff n belongs to A001105.
a(n) = -A340172(n) iff n belongs to A046092.
a(n) = 2*A340172(n) iff n belongs to A139274.
2*a(n) = A340172(n) iff n belongs to A139275.
a(n) * A340172(n) = 0 iff n belongs to A000217.
a(n) = 0 iff n belongs to A014105.
EXAMPLE
The spiral starts as follows:
+-----+-----+-----+-----+-----+
. |
. |
. +-----+-----+-----+ +
. |5 4 3 |2 |
. | | |
+ +-----+-----+ +
|6 | 0 1 | .
| | | .
+ +-----+-----+-----+ .
|7 .
| .
+-----+-----+-----+-----+-----+
8 9 10 11 12 13
- so a(0) = a(3) = a(10) = 0,
- a(1) = a(2) = a(11) = 1.
PROG
(PARI) See Links section.
KEYWORD
sign
AUTHOR
Rémy Sigrist, Dec 30 2020
STATUS
approved