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A293772 Let P be the sequence of distinct lattice points defined by the following rules: P(1) = (0,0), P(2) = (1,0), and for any i < j < k, P(k) does not lie on the vector (P(i), P(j)), and for any n > 2, P(n) is the closest lattice point to P(n-1) such that the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)), say t, satisfies 0 < t <= Pi/2, and in case of a tie, minimize the angle t; a(n) = X-coordinate of P(n). 2
0, 1, 1, 0, -1, -1, 0, 2, 2, 1, 0, -1, -2, -2, -1, 1, 3, 3, 2, 1, -1, -2, -3, -3, -2, -1, 1, 2, 4, 4, 3, 2, 0, -3, -4, -4, -3, -2, -1, 1, 2, 3, 4, 4, 3, 1, -2, -5, -5, -4, -1, 0, 1, 3, 4, 5, 5, 4, 3, 1, -2, -3, -6, -6, -5, -3, 0, 1, 2, 3, 4, 5, 5, 4, 2, -1, -4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

See A293773 for the corresponding Y-coordinates.

The following diagram depicts the angle t cited in the name:

.      P(n)*    .

.          | t .

.          |  .

.          | .

.          |.

.    P(n-1)*

.         /

.        /

. P(n-2)*

This sequence has building features in common with A293680.

The representation of the first thousands points of the sequence shows a spiral.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Representation of P(n) for n=1..100, with lines joining consecutive points

Rémy Sigrist, Representation of P(n) for n=1..1000, with lines joining consecutive points

Rémy Sigrist, Representation of P(n) for n=1..100000

Rémy Sigrist, Scatterplot of a(n) for n=1..100000

Rémy Sigrist, Scatterplot of (n, a(n)) when A293773(n) >= 0 and n <= 100000

Rémy Sigrist, Scatterplot of (n, a(n)) when A293773(n) < 0 and n <= 100000

Rémy Sigrist, PARI program for A293772

EXAMPLE

See representation of first points in Links section.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A293680, A293773.

Sequence in context: A253262 A015504 A055892 * A293680 A293539 A292469

Adjacent sequences:  A293769 A293770 A293771 * A293773 A293774 A293775

KEYWORD

sign,look

AUTHOR

Rémy Sigrist, Oct 16 2017

STATUS

approved

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Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)