Fractran
Fractran (originally styled FRACTRAN) is an esoteric model of computation invented by John Conway in 1987.[1] In this model a program is simply a finite list of fractions, the program state is an integer. For more details see https://en.wikipedia.org/wiki/FRACTRAN
BB_fractran(n) or BBf(n) is the Busy Beaver function for Fractran programs. Specifically, it is the longest runtime for all halting fractran programs of size n when started with state = 2. In this context we consider the size of a fractran program to be the total number of fractions plus the total number of prime factors (counting multiplicity) of all numerators and denominators of all fractions.
Champions
| n | BBf(n) | Example Champion(s) |
|---|---|---|
| 1 | 0 | [1/1]
|
| 2 | 1 | [1/2]
|
| 3 | 1 | [1/2]
|
| 4 | 1 | [1/2]
|
| 5 | 2 | [3/2, 1/3]
|
| 6 | 3 | [9/2, 1/3]
|
| 7 | 4 | [27/2, 1/3]
|
| 8 | 5 | [81/2, 1/3]
|
| 9 | 6 | [243/2, 1/3]
|
| 10 | 7 | [729/2, 1/3]
|
| 11 | 10 | [27/2, 25/3, 1/5]
|
| 12 | 13 | [81/2, 25/3, 1/5]
|
| 13 | 17 | [81/2, 125/3, 1/5]
|
| 14 | 21 | [243/2, 125/3, 1/5]
|
| 15 | 28 | [1/45, 4/5, 3/2, 25/3]
|
| 16 | 53 | [1/45, 4/5, 3/2, 125/3]
|
| 17 | 107 | [5/6, 49/2, 3/5, 40/7]
|
| 18 | 211 | [5/6, 49/2, 3/5, 80/7]
|
| 19 | ≳ 370 | [5/6, 49/2, 3/5, 160/7]
|
References
- ↑ Conway, John H. (1987). "FRACTRAN: A Simple Universal Programming Language for Arithmetic". Open Problems in Communication and Computation. Springer-Verlag New York, Inc. pp. 4–26. http://doi.org/10.1007/978-1-4612-4808-8_2