1RB2LA1RA1RA 1LB1LA3RB1RZ: Difference between revisions
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It runs for 3,932,964 steps and leaves 2,050 ones. | It runs for 3,932,964 steps and leaves 2,050 ones. | ||
== Analysis == | == Analysis by Pascal Michel == | ||
<pre> | |||
Let C(n, 1) = . . . 0 (A0) 2^n 1 0 . . . , | |||
and C(n, 2) = . . . 0 (A0) 2^n 1 1 0 . . . | |||
Then we have: | |||
. . . 0 (A0) 0 . . . --( 6 )--> C(1, 2) | |||
C(3k, 1) --( 15k^2 + 9k + 3 )--> C(5k + 1, 1) | |||
C(3k + 1, 1) --( 15k^2 + 24k + 13 )--> . . . 0 1 3^(5k+2) 1 (H1) 0 . . . | |||
C(3k + 2, 1) --( 15k^2 + 29k + 17 )--> C(5k + 4, 2) | |||
C(3k, 2) --( 15k^2 + 11k + 3 )--> C(5k + 1, 2) | |||
C(3k + 1, 2) --( 15k^2 + 21k + 7 )--> C(5k + 3, 1) | |||
C(3k + 2, 2) --( 15k^2 + 36k + 23 )--> . . . 0 1 3^(5k+4) 1 (H1) 0 . . . | |||
So we have: | |||
. . . 0 (A0) 0 . . . --( 6 )--> | |||
C( 1, 2 ) --( 7 )--> | |||
C( 3, 1 ) --( 27 )--> | |||
C( 6, 1 ) --( 81 )--> | |||
C( 11, 1 ) --( 239 )--> | |||
C( 19, 2 ) --( 673 )--> | |||
C( 33, 1 ) --( 1,917 )--> | |||
C( 56, 1 ) --( 5,399 )--> | |||
C( 94, 2 ) --( 15,073 )--> | |||
C( 158, 1 ) --( 42,085 )--> | |||
C( 264, 2 ) --( 117,131 )--> | |||
C( 441, 2 ) --( 325,755 )--> | |||
C( 736, 2 ) --( 905,527 )--> | |||
C( 1228, 1 ) --( 2,519,044 )--> | |||
. . . 0 1 3^2047 1 (H1) 0 . . . | |||
</pre> | |||
Revision as of 12:25, 7 December 2025
1RB2LA1RA1RA_1LB1LA3RB--- (bbch) is the BB(2,4) champion. It was found in 2005 by Terry and Shawn Ligocki.
It runs for 3,932,964 steps and leaves 2,050 ones.
Analysis by Pascal Michel
Let C(n, 1) = . . . 0 (A0) 2^n 1 0 . . . , and C(n, 2) = . . . 0 (A0) 2^n 1 1 0 . . . Then we have: . . . 0 (A0) 0 . . . --( 6 )--> C(1, 2) C(3k, 1) --( 15k^2 + 9k + 3 )--> C(5k + 1, 1) C(3k + 1, 1) --( 15k^2 + 24k + 13 )--> . . . 0 1 3^(5k+2) 1 (H1) 0 . . . C(3k + 2, 1) --( 15k^2 + 29k + 17 )--> C(5k + 4, 2) C(3k, 2) --( 15k^2 + 11k + 3 )--> C(5k + 1, 2) C(3k + 1, 2) --( 15k^2 + 21k + 7 )--> C(5k + 3, 1) C(3k + 2, 2) --( 15k^2 + 36k + 23 )--> . . . 0 1 3^(5k+4) 1 (H1) 0 . . . So we have: . . . 0 (A0) 0 . . . --( 6 )--> C( 1, 2 ) --( 7 )--> C( 3, 1 ) --( 27 )--> C( 6, 1 ) --( 81 )--> C( 11, 1 ) --( 239 )--> C( 19, 2 ) --( 673 )--> C( 33, 1 ) --( 1,917 )--> C( 56, 1 ) --( 5,399 )--> C( 94, 2 ) --( 15,073 )--> C( 158, 1 ) --( 42,085 )--> C( 264, 2 ) --( 117,131 )--> C( 441, 2 ) --( 325,755 )--> C( 736, 2 ) --( 905,527 )--> C( 1228, 1 ) --( 2,519,044 )--> . . . 0 1 3^2047 1 (H1) 0 . . .