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A326170
Let z be a sequence of distinct Gaussian integers such that z(1) = 0, z(2) = 2+i (where i denotes the imaginary unit), for n > 1, z(n+1) the Gaussian integer with least norm at one knight move from z(n) (in case of a tie, choose the value such that Im(z(n+1)/z(n))>0); a(n) is the real part of z(n).
2
0, 2, 1, 0, -1, 1, -1, 0, 1, -1, 0, 2, 3, 1, 2, 1, 3, 2, 0, -1, -2, -1, -3, -2, -1, -3, -4, -2, 0, -2, 0, 2, 4, 3, 2, 0, -2, -3, -2, 0, 2, 4, 3, 1, -1, -2, -3, -4, -3, -1, 1, 3, 4, 3, 1, -1, -3, -4, -5, -3, -1, 1, 3, 4, 5, 4, 2, 0, -2, -4, -5, -6, -4, -5, -4
OFFSET
1,2
COMMENTS
This sequence is inspired by A316667.
Two Gaussian integers, say u and v, are at one knight move from each other when {abs(Re(u-v)), abs(Im(u-v))} = {1,2}.
The sequence is finite and has 37287 terms; at z(37287) = -23 + 99*i, the knight is trapped.
LINKS
Rémy Sigrist, Figure showing the complete sequence (the black pixel at position X=-23 and Y=99 corresponds to the last term)
EXAMPLE
See illustrations in Links section.
PROG
(PARI) See Links section.
CROSSREFS
See A326171 for the imaginary part.
Cf. A316667.
Sequence in context: A298601 A016366 A016427 * A243841 A131038 A016353
KEYWORD
sign,fini
AUTHOR
Rémy Sigrist, Jun 10 2019
STATUS
approved