login
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.
2
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).
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
KEYWORD
nonn
AUTHOR
WG Zeist, Jan 26 2018
STATUS
approved