Fractran

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway.

A FRACTRAN program is an ordered list of positive fractions P = (f₁, f₂, ... , f_n), together with an initial positive integer input n.

The program is run by updating the integer n as follows:

for the first fraction f in the list for which nf is an integer, replace n by nf ;
repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt.

Conway gave a program for primes in FRACTRAN:

17/91 78/85 19/51 23/38 29/33 77/29 95/23 77/19 1/17 11/13 13/11 15/14 15/2 55/1

Starting with n=2, this FRACTRAN program will change n in 15=15/2*2, then 825=55/1*15, generating the following sequence of integers:

2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, ...

After 2, this sequence contains the following powers of 2:

2²=4, 2³=8, 2^⁵=32, 2^⁷=128, 2¹¹=2048,\, 2¹³=8192,\, 2¹⁷=131072,\, 2¹⁹=524288,...

which are the prime powers of 2.

More on how to program FRACTRAN as a universal programming language will be find in the references.

Your task is to 
write a program that reads a list of fractions in a natural format from the keyboard or from a string, 
to parse it into a sequence of fractions (i.e. two integers),
and runs the FRACTRAN starting from a provided integer, writing the result at each step.  
It a also required that the number of step is limited (by a parameter easy to find).

JavaScript

<lang javascript> var num = new Array(); var den = new Array(); var val ;

function compile(prog){

 var regex = /\s*(\d*)\s*\/\s*(\d*)\s*(.*)/m;
 while(regex.test(prog)){
   num.push(regex.exec(prog)[1]);
   den.push(regex.exec(prog)[2]);
   prog = regex.exec(prog)[3];
 }

}

function dump(prog){

 for(var i=0; i<num.length; i++)
   document.body.innerHTML += num[i]+"/"+den[i]+" ";
 document.body.innerHTML += "
";

}

function step(val){

 var i=0;
 while(i<den.length && val%den[i] != 0) i++;
 return num[i]*val/den[i];

}

function exec(val){

 var i = 0;
 while(val && i<limit){
   document.body.innerHTML += i+": "+val+"
";
   val = step(val);
   i ++;
 }

}

// Main compile("17/91 78/85 19/51 23/38 29/33 77/29 95/23 77/19 1/17 11/13 13/11 15/14 15/2 55/1"); dump(); var limit = 15; exec(2); </lang>

References

J. H. Conway (1987). Fractran: A Simple Universal Programming Language for Arithmetic. In: Open Problems in Communication and Computation, pages 4–26. Springer.

J. H. Conway (2010). "FRACTRAN: A simple universal programming language for arithmetic". In Jeffrey C. Lagarias. The Ultimate Challenge: the 3x+1 problem. American Mathematical Society. pp. 249–264. ISBN 978-0-8218-4940-8. Zbl 1216.68068.