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

Author

Oleg Nikulin, Jul 22 2016

Keywords

• nonn

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

Crossrefs

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

Formula

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