A275304 Intervals between iterations at which Langton's Ant living on triangular tiling reaches the distance of n from the origin for the first time.

1, 1, 1, 11, 1, 33, 5, 83, 9, 217, 13, 99, 17, 233, 21, 1159, 17, 313, 33, 95, 21, 117, 37, 249, 25, 731, 33, 4729, 21, 107, 69, 447, 41, 5869, 53, 345, 53, 2949, 109, 3437, 217, 359, 73, 769, 57, 10181, 81, 2291, 97, 3217, 73, 6445, 105, 493, 81, 6035, 113

Offset

1,4

Comments

The distance is defined as the number of steps needed to reach the origin (analog of Manhattan distance). It seems that starting from n=625 (which corresponds to iterations around 26,000,000), a(n)=53 for odd n. [amended by Andrey Zabolotskiy, Oct 09 2016]

Links

Andrey Zabolotskiy, Table of n, a(n) for n = 1..1500 (calculated using Oleg Nikulin's program)

Wikipedia, Turmite

Formula

a(n) = A275303(n) - A275303(n-1).

Crossrefs

Cf. A269757, A275302, A275303 (cumulative sums), A275305.

Sequence in context: A174221 A194039 A298084 * A245677 A182041 A086994

Adjacent sequences: A275301 A275302 A275303 * A275305 A275306 A275307

Keyword

nonn

Author

Oleg Nikulin, Jul 22 2016

Status

approved