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A322574
z(1) = 0, and for any n > 0, z(4*n-2) = z(n) + k(n), z(4*n-1) = z(n) + i*k(n), z(4*n) = z(n) - k(n) and z(4*n+1) = z(n) - i*k(n) where k(n) is the least positive integer not leading to a duplicate term in sequence z (and i denotes the imaginary unit); a(n) is the real part of z(n).
4
0, 1, 0, -1, 0, 4, 1, -2, 1, 3, 0, -3, 0, 2, -1, -4, -1, 3, 0, -3, 0, 5, 4, 3, 4, 2, 1, 0, 1, 6, -2, -10, -2, 2, 1, 0, 1, 7, 3, -1, 3, 9, 0, -9, 0, -2, -3, -4, -3, 7, 0, -7, 0, 9, 2, -5, 2, 3, -1, -5, -1, 7, -4, -15, -4, 4, -1, -6, -1, 8, 3, -2, 3, 8, 0, -8, 0
OFFSET
1,6
COMMENTS
Will z run through every Gaussian integer?
EXAMPLE
The first terms, alongside z(n), k(n) and associate children, are:
n a(n) z(n) k z(4*n-2) z(4*n-1) z(4*n) z(4*n+1)
-- ---- ------- - -------- -------- ------ --------
1 0 0 1 1 i -1 -i
2 1 1 3 4 1 + 3*i -2 1 - 3*i
3 0 i 3 3 + i 4*i -3 + i -2*i
4 -1 -1 3 2 -1 + 3*i -4 -1 - 3*i
5 0 -i 3 3 - i 2*i -3 - i -4*i
6 4 4 1 5 4 + i 3 4 - i
7 1 1 + 3*i 1 2 + 3*i 1 + 4*i 3*i 1 + 2*i
8 -2 -2 8 6 -2 + 8*i -10 -2 - 8*i
9 1 1 - 3*i 1 2 - 3*i 1 - 2*i -3*i 1 - 4*i
10 3 3 + i 4 7 + i 3 + 5*i -1 + i 3 - 3*i
PROG
(PARI) \\ See Links section.
CROSSREFS
See A322575 for the imaginary part of z.
This sequence is a complex variant of A322510.
Sequence in context: A247004 A010640 A244424 * A030787 A176218 A109008
KEYWORD
sign
AUTHOR
Rémy Sigrist, Dec 17 2018
STATUS
approved