OFFSET
1,8
COMMENTS
See A293540 for the Y-coordinate of P(n).
The following diagram depicts the angle t cited in the name:
. P(n)* .
. | t .
. | .
. | .
. |.
. P(n-1)*
. /
. /
. P(n-2)*
The sequence P has similarities with Langton's ant:
- after an apparently chaotic initial phase, an escape consisting of a repetitive pattern emerges at n = 9118 (see illustrations in Links section),
- more formally: P(n+258) = P(n) + (14,-8) for any n >= 9118,
- See also A293207 for other sequences of points with emerging escapes.
See also A292469 for a sequence of points with similar construction features.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..12000
Wikipedia, Langton's ant
Rémy Sigrist, Colorized representation of the points P'(n) of the variant where we maximize the angle t in case of a tie for n=1..1000000
Rémy Sigrist, PARI program for A293539
FORMULA
a(n + 258) = a(n) + 14 for any n >= 9118.
EXAMPLE
See representation of first points in Links section.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign,look
AUTHOR
Rémy Sigrist, Oct 11 2017
STATUS
approved