

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(n1) such that the angle of the vectors (P(n2), P(n1)) and (P(n1), P(n)), say t, satisfies 0 < t <= Pi/2, and in case of a tie, minimize the angle t; a(n) = Xcoordinate 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
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OFFSET

1,8


COMMENTS

See A293773 for the corresponding Ycoordinates.
The following diagram depicts the angle t cited in the name:
. P(n)* .
.  t .
.  .
.  .
. .
. P(n1)*
. /
. /
. P(n2)*
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



