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).

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

Table of n, a(n) for n=1..75.

Rémy Sigrist, Illustration of the first 100 terms

Rémy Sigrist, Figure showing the complete sequence (the black pixel at position X=-23 and Y=99 corresponds to the last term)

Rémy Sigrist, PARI program for A326170

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

Adjacent sequences: A326167 A326168 A326169 * A326171 A326172 A326173

Keyword

sign,fini

Author

Rémy Sigrist, Jun 10 2019

Status

approved