Some FRACTRAN programs in case we ever have a category for it

## A+B[edit]

Input a number of the form 2^a 3^b

2/3

The output is 2^(a+b)

## Empty program[edit]

A list of no fractions does nothing, then immediately stops.

## Integer Sequence[edit]

Given the number 1 as input the following program will, as its (3n-2)th step, produce the number 2^n.

2/3, 9/2, 2/1

## Logical operations[edit]

It's not so hard to code up all sixteen possible two-input logic gates, so here they are. The input is 2^a 3^b where a,b are zero or one and the output is 5^1 for true and 5^0 for false. Gates that return true when all their inputs are false additionally require the flag 11 to be set as input (ie 2^a*3^b*11)- any FRACTRAN program with the number 1 as input either stops without doing anything or loops forever.

5/6, 1/2, 1/3 AND gate

5/6, 5/2, 5/3 OR gate

1/22, 5/11 NOT gate (uses 11 as a halt flag, result of 2^a*11 is 5^not(a))

1/6, 5/2, 5/3 XOR gate

1/66, 5/22, 5/33, 5/11 NAND gate (needs 11 flag)

5/66, 1/22, 1/33, 5/11 NXOR gate (needs flag)

1/66, 1/22, 1/33, 5/11 NOR gate (needs flag)

so much for all the commonly encountered ones, but there's still another eight to go. Most are obscure and of limited utility.

1/2, 1/3 ZERO gate, returns false regardless of its input

1/6, 5/2, 1/3 "A and not B", true only if A is true and B is false

5/2, 1/3 A , returns the state of A regardless of B

1/6, 1/2, 5/3 "B and not A", true only if B is true and A is false

1/2, 5/3 B , returns the state of B regardless of A

1/66, 1/33, 5/11 "A or not B" (needs flag)

1/66, 1/22, 5/11 "B or not A" (needs flag)

5/66, 5/22, 5/33, 5/11 ONE gate, returns true regardless of its input, needs flag

NOT A and NOT B are omitted because the one-input NOT gate is already up there.

## Sort three variables[edit]

FRACTRAN's only data type is positive integers. Suppose (a,b,c) are the integers to be sorted. Give the following as input: 2^a 3^b 5^c

1001/30, 143/6, 143/10, 143/15, 13/2, 13/3, 13/5

Returns 7^A 11^B 13^C where (A,B,C) are (a,b,c) in ascending order.