A231427 Minimum number of live cells in Conway's Game of Life that is a nontrivial oscillator of period n.

4, 3, 12, 12, 15, 16, 28, 12, 29, 24, 33, 33, 34, 16, 12, 21, 36, 43, 92, 30, 32, 36, 55, 24, 30, 60, 56, 46, 54, 20, 48, 45, 46, 74, 44, 22, 58, 42, 46, 26, 204

Offset

1,1

Comments

Oscillators are nontrivial in the sense that there must be at least one cell that oscillates at the full period. See the LifeWiki website for diagrams of these oscillators.

Most of these terms are only the smallest known values and are not proved to be the minimum. - Eric M. Schmidt, Nov 22 2013

Which of these terms are actually known? - Charles R Greathouse IV, Jun 17 2020

Links

Table of n, a(n) for n=1..41.

LifeWiki, Oscillator

LifeWiki, Rob's p16

LifeWiki, Cribbage

Wikipedia, Conway's Game of Life

Example

The "blinker" is the smallest period 2 nontrivial oscillator.
Its generations have 3 cells:
. . . . . | . . . . .
. . . . . | . . o . .
. o o o . | . . o . .
. . . . . | . . o . .
. . . . . | . . . . .
Therefore a(2) = 3.
The "caterer" is the smallest period 3 oscillator.
Its generations have 12, 15, and 16 cells:
. . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
. . . . o . . . . . . | . . . . . . . o o . . | . . . . . . . . o . .
. . o . . . o o o o . | . . . o . o o o o . . | . . . o o o . . . o .
. . o . . . o . . . . | . o o o . . o . o . . | . . o o o o o . o . .
. . o . . . . . . . . | . . . . . . . . . . . | . . . . o . . . . . .
. . . . . o . . . . . | . . . o o . . . . . . | . . . o o . . . . . .
. . . o o . . . . . . | . . . . o . . . . . . | . . . o o . . . . . .
. . . . . . . . . . . | . . . . . . . . . . . | . . . . . . . . . . .
Therefore a(3) = 12.

Crossrefs

Sequence in context: A205371 A270633 A272220 * A215942 A054908 A141826

Adjacent sequences: A231424 A231425 A231426 * A231428 A231429 A231430

Keyword

nonn,hard,nice,more

Author

Arkadiusz Wesolowski, Nov 19 2013

Extensions

a(17) [= 36, Sep 2014 discovery of Merzenich] corrected by Eric M. Schmidt, Nov 15 2014

a(11) [= 33, Jan 2016 discovery of Dean Hickerson] corrected by Nathaniel Johnston, Dec 03 2019

a(16) [= 21, Feb 2020 discovery of Rob Liston] corrected by Oscar Cunningham, Jun 16 2020

a(19)-a(41) from Sergio Pimentel, Aug 09 2023

Status

approved