A298819 a(n) is the period of the oscillating pattern formed by a 1 X n line of cells in the Life-like cellular automaton B2c3-cekq4ikt5i8/S2-in3-acky4aijry5eiky6i, or 0 if the pattern vanishes.

0, 0, 2, 2, 2, 0, 6, 6, 12, 4, 28, 14, 14, 0, 14, 14, 84, 12, 372, 62, 248, 8, 504, 126, 252, 28, 420, 30, 30, 0, 30, 30, 420, 28, 2044, 1022, 12264, 24, 504, 126, 7812, 124, 253828, 4094, 32752, 16, 16368, 2046, 85932, 252, 18396, 1022, 4088, 56, 917448, 32766, 327660, 60, 1860, 62, 62, 0, 62, 62

Offset

1,3

Comments

An explanation of the Hensel notation used to define the cellular automaton rule can be found on the LifeWiki (see links).

Links

Table of n, a(n) for n=1..64.

LifeWiki, Isotropic non-totalistic Life-like cellular automaton

Formula

For n divisible by 4, a(n) = A160657(n/4) = (a divisor of) 2^(A003558(n/4) + 1) - 2.

With the exception of a(1), all values of n for which a(n) = 0 are of the form 2^m - 2 for some integer m (A000918).

a(2k) = A268754(k); a(2k+1) = lcm(A268754(k), A268754(k+1)) (conjectured). Note that, by an arbitrary/cosmetic convention, A268754 uses 1 for empty patterns and A298819 uses 0. - WG Zeist and Charlie Neder, Jan 11 2019

Example

a(4) = 2 because a 1 X 4 line oscillates with period 2 in this cellular automaton.

Crossrefs

Cf. A000918, A003558, A160657, A268754.

Sequence in context: A011139 A136663 A165490 * A307520 A265648 A181230

Adjacent sequences: A298816 A298817 A298818 * A298820 A298821 A298822

Keyword

nonn

Author

WG Zeist, Jan 26 2018

Status

approved