Fractran
You are encouraged to solve this task according to the task description, using any language you may know.
FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Horton Conway.
A FRACTRAN program is an ordered list of positive fractions , together with an initial positive integer input .
The program is run by updating the integer as follows:
- for the first fraction, , in the list for which is an integer, replace by ;
- repeat this rule until no fraction in the list produces an integer when multiplied by , then halt.
Conway gave a program for primes in FRACTRAN:
- , , , , , , , , , , , , ,
Starting with , this FRACTRAN program will change in , then , generating the following sequence of integers:
- , , , , , , , , , , ,
After 2, this sequence contains the following powers of 2:
- , , , , , , , ,
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 is also required that the number of step is limited (by a parameter easy to find).
Extra credit: Use this program to derive the first 20 or so prime numbers.
- 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.
- Number Pathology: Fractran by Mark C. Chu-Carroll; October 27, 2006.
AutoHotkey
<lang AutoHotkey>n := 2, steplimit := 15, numerator := [], denominator := [] s := "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"
Loop, Parse, s, % A_Space
if (!RegExMatch(A_LoopField, "^(\d+)/(\d+)$", m))
MsgBox, % "Invalid input string (" A_LoopField ")."
else
numerator[A_Index] := m1, denominator[A_Index] := m2
SetFormat, FloatFast, 0.0 Gui, Add, ListView, R10 W100 -Hdr, | SysGet, VSBW, 2 LV_ModifyCol(1, 95 - VSBW), LV_Add( , 0 ": " n) Gui, Show
Loop, % steplimit {
i := A_Index
Loop, % numerator.MaxIndex()
if (!Mod(nn := n * numerator[A_Index] / denominator[A_Index], 1)) {
LV_Modify(LV_Add( , i ": " (n := nn)), "Vis")
continue, 2
}
break
}</lang> Output:
0: 2 1: 15 2: 825 3: 725 4: 1925 5: 2275 6: 425 7: 390 8: 330 9: 290 10: 770 11: 910 12: 170 13: 156 14: 132 15: 116
C
Using GMP. Powers of two are in brackets. For extra credit, pipe the output through | less -S.
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <gmp.h>
typedef struct frac_s *frac; struct frac_s { int n, d; frac next; };
frac parse(char *s) { int offset = 0; struct frac_s h = {0}, *p = &h;
while (2 == sscanf(s, "%d/%d%n", &h.n, &h.d, &offset)) { s += offset; p = p->next = malloc(sizeof *p); *p = h; p->next = 0; }
return h.next; }
int run(int v, char *s) { frac n, p = parse(s); mpz_t val; mpz_init_set_ui(val, v);
loop: n = p; if (mpz_popcount(val) == 1) gmp_printf("\n[2^%d = %Zd]", mpz_scan1(val, 0), val); else gmp_printf(" %Zd", val);
for (n = p; n; n = n->next) { // assuming the fractions are not reducible if (!mpz_divisible_ui_p(val, n->d)) continue;
mpz_divexact_ui(val, val, n->d); mpz_mul_ui(val, val, n->n); goto loop; }
gmp_printf("\nhalt: %Zd has no divisors\n", val);
mpz_clear(val); while (p) { n = p->next; free(p); p = n; }
return 0; }
int main(void) { run(2, "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");
return 0; }</lang>
C++
<lang cpp>
- include <iostream>
- include <sstream>
- include <iterator>
- include <vector>
- include <math.h>
using namespace std;
class fractran { public:
void run( std::string p, int s, int l )
{
start = s; limit = l;
istringstream iss( p ); vector<string> tmp;
copy( istream_iterator<string>( iss ), istream_iterator<string>(), back_inserter<vector<string> >( tmp ) );
string item; vector< pair<float, float> > v;
pair<float, float> a; for( vector<string>::iterator i = tmp.begin(); i != tmp.end(); i++ ) { string::size_type pos = ( *i ).find( '/', 0 ); if( pos != std::string::npos ) { a = make_pair( atof( ( ( *i ).substr( 0, pos ) ).c_str() ), atof( ( ( *i ).substr( pos + 1 ) ).c_str() ) ); v.push_back( a ); } }
exec( &v );
}
private:
void exec( vector< pair<float, float> >* v )
{
int cnt = 0; bool found; float r; while( cnt < limit ) { cout << cnt << " : " << start << "\n"; cnt++; vector< pair<float, float> >::iterator it = v->begin(); found = false; while( it != v->end() ) { r = start * ( ( *it ).first / ( *it ).second ); if( r == floor( r ) ) { found = true; break; } ++it; }
if( found ) start = ( int )r; else break; }
} int start, limit;
}; int main( int argc, char* argv[] ) {
fractran f; f.run( "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", 2, 15 ); return system( "pause" );
} </lang>
- Output:
0 : 2 1 : 15 2 : 825 3 : 725 4 : 1925 5 : 2275 6 : 425 7 : 390 8 : 330 9 : 290 10 : 770 11 : 910 12 : 170 13 : 156 14 : 132
Common Lisp
<lang lisp>(defun fractran (n frac-list)
(lambda ()
(prog1
n
(when n
(let ((f (find-if (lambda (frac)
(integerp (* n frac)))
frac-list)))
(when f (setf n (* f n))))))))
- test
(defvar *primes-ft* '(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))
(loop with fractran-instance = (fractran 2 *primes-ft*)
repeat 20
for next = (funcall fractran-instance)
until (null next)
do (print next))</lang>
Output:
2 15 825 725 1925 2275 425 390 330 290 770 910 170 156 132 116 308 364 68 4
D
Simple Version
<lang d>import std.stdio, std.algorithm, std.conv, std.array;
void fractran(in string prog, int val, in uint limit) {
const fracts = prog.split.map!(p => p.split("/").to!(int[])).array;
foreach (immutable n; 0 .. limit) {
writeln(n, ": ", val);
const found = fracts.find!(p => val % p[1] == 0);
if (found.empty)
break;
val = found.front[0] * val / found.front[1];
}
}
void main() {
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", 2, 15);
}</lang>
- Output:
0: 2 1: 15 2: 825 3: 725 4: 1925 5: 2275 6: 425 7: 390 8: 330 9: 290 10: 770 11: 910 12: 170 13: 156 14: 132
Lazy Version
<lang d>import std.stdio, std.algorithm, std.conv, std.array, std.range;
struct Fractran {
int front; bool empty = false; const int[][] fracts;
this(in string prog, in int val) {
this.front = val;
fracts = prog.split.map!(p => p.split("/").to!(int[])).array;
}
void popFront() {
const found = fracts.find!(p => front % p[1] == 0);
if (found.empty)
empty = true;
else
front = found.front[0] * front / found.front[1];
}
}
void main() {
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", 2)
.take(15).writeln;
}</lang>
- Output:
[2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132]
Haskell
<lang haskell>import Data.List (find) import Data.Ratio (Ratio, (%), denominator)
fractran :: (Integral a) => [Ratio a] -> a -> [a] fractran fracts n = n :
case find (\f -> n `mod` denominator f == 0) fracts of Nothing -> [] Just f -> fractran fracts $ truncate (fromIntegral n * f)
main :: IO () main = print $ take 15 $ 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] 2</lang>
- Output:
[2,15,825,725,1925,2275,425,390,330,290,770,910,170,156,132]
Icon and Unicon
Works in both languages:
<lang unicon>record fract(n,d)
procedure main(A)
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", 2)
end
procedure fractran(s, n, limit)
execute(parse(s),n, limit)
end
procedure parse(s)
f := []
s ? while not pos(0) do {
tab(upto(' ')|0) ? put(f,fract(tab(upto('/')), (move(1),tab(0))))
move(1)
}
return f
end
procedure execute(f,d,limit)
/limit := 15
every !limit do {
if d := (d%f[i := !*f].d == 0, (writes(" ",d)/f[i].d)*f[i].n) then {}
else break write()
}
write()
end</lang>
Output:
->fractan 2 15 825 725 1925 2275 425 390 330 290 770 910 170 156 132 ->
Java
<lang java>import java.util.Vector; import java.util.regex.Matcher; import java.util.regex.Pattern;
public class Fractran{
public static void main(String []args){
new 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", 2);
}
final int limit = 15;
Vector<Integer> num = new Vector<>();
Vector<Integer> den = new Vector<>();
public Fractran(String prog, Integer val){
compile(prog);
dump();
exec(2);
}
void compile(String prog){
Pattern regexp = Pattern.compile("\\s*(\\d*)\\s*\\/\\s*(\\d*)\\s*(.*)");
Matcher matcher = regexp.matcher(prog);
while(matcher.find()){
num.add(Integer.parseInt(matcher.group(1)));
den.add(Integer.parseInt(matcher.group(2)));
matcher = regexp.matcher(matcher.group(3));
}
}
void exec(Integer val){
int n = 0;
while(val != null && n<limit){
System.out.println(n+": "+val);
val = step(val);
n++;
}
}
Integer step(int val){
int i=0;
while(i<den.size() && val%den.get(i) != 0) i++;
if(i<den.size())
return num.get(i)*val/den.get(i);
return null;
}
void dump(){
for(int i=0; i<den.size(); i++)
System.out.print(num.get(i)+"/"+den.get(i)+" ");
System.out.println();
}
}</lang>
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>
Perl
Instead of printing all steps, I chose to only print those steps which were a power of two. This makes the fact that it's a prime-number-generating program much clearer.
<lang perl>use strict; use warnings; use Math::BigRat;
my ($n, @P) = map Math::BigRat->new($_), qw{ 2 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 };
$|=1; MAIN: for( 1 .. 5000 ) { print " " if $_ > 1; my ($pow, $rest) = (0, $n->copy); until( $rest->is_odd ) { ++$pow; $rest->bdiv(2); } if( $rest->is_one ) { print "2**$pow"; } else { #print $n; } for my $f_i (@P) { my $nf_i = $n * $f_i; next unless $nf_i->is_int; $n = $nf_i; next MAIN; } last; }
print "\n"; </lang>
If you uncomment the
#print $n
, it will print all the steps.
Perl 6
A Fractran program potentially returns an infinite list, and infinite lists are a common data structure in Perl 6. The limit is therefore enforced only by slicing the infinite list. <lang perl6>sub ft (\n) {
first Int, map (* * n).narrow,
<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>, 0
} constant FT = 2, &ft ... 0; say FT[^100];</lang>
- Output:
2 15 825 725 1925 2275 425 390 330 290 770 910 170 156 132 116 308 364 68 4 30 225 12375 10875 28875 25375 67375 79625 14875 13650 2550 2340 1980 1740 4620 4060 10780 12740 2380 2184 408 152 92 380 230 950 575 2375 9625 11375 2125 1950 1650 1450 3850 4550 850 780 660 580 1540 1820 340 312 264 232 616 728 136 8 60 450 3375 185625 163125 433125 380625 1010625 888125 2358125 2786875 520625 477750 89250 81900 15300 14040 11880 10440 27720 24360 64680 56840 150920 178360 33320 30576 5712 2128 1288
Extra credit:
We can weed out all the powers of two into another infinite constant list based on the first list. In this case the sequence is limited only by our patience, and a ^C from the terminal. The .msb method finds the most significant bit of an integer, which conveniently is the base-2 log of the power-of-two in question. <lang perl6>constant FT2 = FT.grep: { not $_ +& ($_ - 1) } for 1..* -> $i {
given FT2[$i] {
say $i, "\t", .msb, "\t", $_;
}
}</lang>
- Output:
1 2 4 2 3 8 3 5 32 4 7 128 5 11 2048 6 13 8192 7 17 131072 8 19 524288 9 23 8388608 10 29 536870912 11 31 2147483648 12 37 137438953472 13 41 2199023255552 14 43 8796093022208 15 47 140737488355328 16 53 9007199254740992 17 59 576460752303423488 18 61 2305843009213693952 19 67 147573952589676412928 20 71 2361183241434822606848 ^C
Python
<lang python>from fractions import Fraction
def fractran(n, fstring='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'):
flist = [Fraction(f) for f in fstring.replace(' ', ).split(',')]
yield n
while True:
for f in flist:
if (n * f).denominator == 1:
break
else:
break
n *= f
yield n.numerator
if __name__ == '__main__':
n, m = 2, 15
print('First %i members of fractran(%i):\n ' % (m, n) +
', '.join(str(f) for f,i in zip(fractran(n), range(m))))</lang>
- Output:
First 15 members of fractran(2): 2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132
Racket
Simple version, without sequences.
<lang Racket>#lang racket
(define (displaysp x)
(display x) (display " "))
(define (read-string-list str)
(map string->number
(string-split (string-replace str " " "") ",")))
(define (eval-fractran n list)
(for/or ([e (in-list list)])
(let ([en (* e n)])
(and (integer? en) en))))
(define (show-fractran fr n s)
(printf "First ~a members of fractran(~a):\n" s n)
(displaysp n)
(for/fold ([n n]) ([i (in-range (- s 1))])
(let ([new-n (eval-fractran n fr)])
(displaysp new-n)
new-n))
(void))
(define fractran
(read-string-list
(string-append "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")))
(show-fractran fractran 2 15)</lang>
- Output:
First 15 members of fractran(2): 2 15 825 725 1925 2275 425 390 330 290 770 910 170 156 132
REXX
Programming note: extra blanks can be inserted in the fractions before and/or after the solidus [/].
showing all terms
<lang rexx>/*REXX pgm runs FRACTAN for a given set of fractions and from a given N.*/ numeric digits 1000 /*be able to handle larger nums. */ parse arg N terms fracs /*get optional arguments from CL.*/ if N== | N==',' then N=2 /*N specified? No, use default.*/ if terms==|terms==',' then terms=100 /*TERMS specified? Use default.*/ if fracs= then fracs= , /*any fractions specified? No···*/ '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' f=space(fracs,0) /* [↑] use default for fractions.*/
do i=1 while f\==; parse var f n.i '/' d.i ',' f
end /*i*/ /* [↑] parse all the fractions.*/
- =i-1 /*the number of fractions found. */
say # 'fractions:' fracs /*display # and actual fractions.*/ say 'N is starting at ' N /*display the starting number N.*/ say terms ' terms are being shown:' /*display a kind of header/title.*/
do j=1 for terms /*perform loop once for each term*/
do k=1 for #; if N//d.k\==0 then iterate /*not an integer?*/
say right('term' j,35) '──► ' N /*display the Nth term with N. */
N = N * n.k % d.k /*calculate the next term (use %)*/
leave /*go start calculating next term.*/
end /*k*/ /* [↑] if integer, found a new N*/
end /*j*/
/*stick a fork in it, we're done.*/</lang>
output using the default input:
14 fractions: 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
N is starting at 2
100 terms are being shown:
term 1 ──► 2
term 2 ──► 15
term 3 ──► 825
term 4 ──► 725
term 5 ──► 1925
term 6 ──► 2275
term 7 ──► 425
term 8 ──► 390
term 9 ──► 330
term 10 ──► 290
term 11 ──► 770
term 12 ──► 910
term 13 ──► 170
term 14 ──► 156
term 15 ──► 132
term 16 ──► 116
term 17 ──► 308
term 18 ──► 364
term 19 ──► 68
term 20 ──► 4
term 21 ──► 30
term 22 ──► 225
term 23 ──► 12375
term 24 ──► 10875
term 25 ──► 28875
term 26 ──► 25375
term 27 ──► 67375
term 28 ──► 79625
term 29 ──► 14875
term 30 ──► 13650
term 31 ──► 2550
term 32 ──► 2340
term 33 ──► 1980
term 34 ──► 1740
term 35 ──► 4620
term 36 ──► 4060
term 37 ──► 10780
term 38 ──► 12740
term 39 ──► 2380
term 40 ──► 2184
term 41 ──► 408
term 42 ──► 152
term 43 ──► 92
term 44 ──► 380
term 45 ──► 230
term 46 ──► 950
term 47 ──► 575
term 48 ──► 2375
term 49 ──► 9625
term 50 ──► 11375
term 51 ──► 2125
term 52 ──► 1950
term 53 ──► 1650
term 54 ──► 1450
term 55 ──► 3850
term 56 ──► 4550
term 57 ──► 850
term 58 ──► 780
term 59 ──► 660
term 60 ──► 580
term 61 ──► 1540
term 62 ──► 1820
term 63 ──► 340
term 64 ──► 312
term 65 ──► 264
term 66 ──► 232
term 67 ──► 616
term 68 ──► 728
term 69 ──► 136
term 70 ──► 8
term 71 ──► 60
term 72 ──► 450
term 73 ──► 3375
term 74 ──► 185625
term 75 ──► 163125
term 76 ──► 433125
term 77 ──► 380625
term 78 ──► 1010625
term 79 ──► 888125
term 80 ──► 2358125
term 81 ──► 2786875
term 82 ──► 520625
term 83 ──► 477750
term 84 ──► 89250
term 85 ──► 81900
term 86 ──► 15300
term 87 ──► 14040
term 88 ──► 11880
term 89 ──► 10440
term 90 ──► 27720
term 91 ──► 24360
term 92 ──► 64680
term 93 ──► 56840
term 94 ──► 150920
term 95 ──► 178360
term 96 ──► 33320
term 97 ──► 30576
term 98 ──► 5712
term 99 ──► 2128
term 100 ──► 1288
showing prime numbers
Programming note: If the number of terms specified (the 2nd argument) is negative, then only powers of two are displayed. <lang rexx>/*REXX pgm runs FRACTAN for a given set of fractions and from a given N.*/ numeric digits 999; w=length(digits()) /*be able to handle larger nums. */ parse arg N terms fracs /*get optional arguments from CL.*/ if N== | N==',' then N=2 /*N specified? No, use default.*/ if terms==|terms==',' then terms=100 /*TERMS specified? Use default.*/ if fracs= then fracs= , /*any fractions specified? No···*/ '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' f=space(fracs,0) /* [↑] use default for fractions.*/ tell= terms>0 /*flag: show # or a power of 2.*/
do i=1 while f\==; parse var f n.i '/' d.i ',' f
end /*i*/ /* [↑] parse all the fractions.*/
!.=0 /*default value for powers of 2.*/ if \tell then do p=0 until length(_)>100; _=2**p; !._=1
if p<2 then @._=left(,w+9) '2**'left(p,w) " "
else @._='(prime' right(p,w)") 2**"left(p,w) ' '
end /*p*/ /* [↑] build powers of 2 tables.*/
- =i-1 /*the number of fractions found. */
say # 'fractions:' fracs /*display # and actual fractions.*/ say 'N is starting at ' N /*display the starting number N.*/ if tell then say terms ' terms are being shown:' /*display hdr.*/
else say 'only powers of two are being shown:' /* " " */
do j=1 for abs(terms) /*perform loop once for each term*/
do k=1 for #; if N//d.k\==0 then iterate /*not an integer?*/
if tell then say right('term' j,35) '──► ' N /*display Nth term&N*/
else if !.N then say right('term' j,35) '──►' @.N N /*2↑ⁿ*/
N = N * n.k % d.k /*calculate the next term (use %)*/
leave /*go start calculating next term.*/
end /*k*/ /* [↑] if integer, found a new N*/
end /*j*/
/*stick a fork in it, we're done.*/</lang>
output using the input of: , -22000000
(twenty-two million)
14 fractions: 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
N is starting at 2
only powers of two are being shown:
term 1 2**1 2
term 20 (prime 2) 2**2 4
term 70 (prime 3) 2**3 8
term 281 (prime 5) 2**5 32
term 708 (prime 7) 2**7 128
term 2364 (prime 11) 2**11 2048
term 3877 (prime 13) 2**13 8192
term 8069 (prime 17) 2**17 131072
term 11320 (prime 19) 2**19 524288
term 19202 (prime 23) 2**23 8388608
term 36867 (prime 29) 2**29 536870912
term 45552 (prime 31) 2**31 2147483648
term 75225 (prime 37) 2**37 137438953472
term 101113 (prime 41) 2**41 2199023255552
term 117832 (prime 43) 2**43 8796093022208
term 152026 (prime 47) 2**47 140737488355328
term 215385 (prime 53) 2**53 9007199254740992
term 293376 (prime 59) 2**59 576460752303423488
term 327021 (prime 61) 2**61 2305843009213693952
term 428554 (prime 67) 2**67 147573952589676412928
term 507520 (prime 71) 2**71 2361183241434822606848
term 555695 (prime 73) 2**73 9444732965739290427392
term 700064 (prime 79) 2**79 604462909807314587353088
term 808332 (prime 83) 2**83 9671406556917033397649408
term 989527 (prime 89) 2**89 618970019642690137449562112
term 1273491 (prime 97) 2**97 158456325028528675187087900672
term 1434367 (prime 101) 2**101 2535301200456458802993406410752
term 1530214 (prime 103) 2**103 10141204801825835211973625643008
term 1710924 (prime 107) 2**107 162259276829213363391578010288128
term 1818255 (prime 109) 2**109 649037107316853453566312041152512
term 2019963 (prime 113) 2**113 10384593717069655257060992658440192
term 2833090 (prime 127) 2**127 170141183460469231731687303715884105728
term 3104686 (prime 131) 2**131 2722258935367507707706996859454145691648
term 3546321 (prime 137) 2**137 174224571863520493293247799005065324265472
term 3720786 (prime 139) 2**139 696898287454081973172991196020261297061888
term 4549719 (prime 149) 2**149 713623846352979940529142984724747568191373312
term 4755582 (prime 151) 2**151 2854495385411919762116571938898990272765493248
term 5329875 (prime 157) 2**157 182687704666362864775460604089535377456991567872
term 5958404 (prime 163) 2**163 11692013098647223345629478661730264157247460343808
term 6400898 (prime 167) 2**167 187072209578355573530071658587684226515959365500928
term 7120509 (prime 173) 2**173 11972621413014756705924586149611790497021399392059392
term 7868448 (prime 179) 2**179 766247770432944429179173513575154591809369561091801088
term 8164153 (prime 181) 2**181 3064991081731777716716694054300618367237478244367204352
term 9541986 (prime 191) 2**191 3138550867693340381917894711603833208051177722232017256448
term 9878163 (prime 193) 2**193 12554203470773361527671578846415332832204710888928069025792
term 10494775 (prime 197) 2**197 200867255532373784442745261542645325315275374222849104412672
term 10852158 (prime 199) 2**199 803469022129495137770981046170581301261101496891396417650688
term 12871594 (prime 211) 2**211 3291009114642412084309938365114701009965471731267159726697218048
term 15137114 (prime 223) 2**223 13479973333575319897333507543509815336818572211270286240551805124608
term 15956646 (prime 227) 2**227 215679573337205118357336120696157045389097155380324579848828881993728
term 16429799 (prime 229) 2**229 862718293348820473429344482784628181556388621521298319395315527974912
term 17293373 (prime 233) 2**233 13803492693581127574869511724554050904902217944340773110325048447598592
term 18633402 (prime 239) 2**239 883423532389192164791648750371459257913741948437809479060803100646309888
term 19157411 (prime 241) 2**241 3533694129556768659166595001485837031654967793751237916243212402585239552
term 21564310 (prime 251) 2**251 3618502788666131106986593281521497120414687020801267626233049500247285301248
Output note: There are intermediary numbers (not powers of two) that are hundreds of digits long.
Tcl
<lang tcl>package require Tcl 8.6
oo::class create Fractran {
variable fracs nco
constructor {fractions} {
set fracs {} foreach frac $fractions { if {[regexp {^(\d+)/(\d+),?$} $frac -> num denom]} { lappend fracs $num $denom } else { return -code error "$frac is not a supported fraction" } } if {![llength $fracs]} { return -code error "need at least one fraction" }
}
method execute {n {steps 15}} {
set co [coroutine [incr nco] my Generate $n] for {set i 0} {$i < $steps} {incr i} { lappend result [$co] } catch {rename $co ""} return $result
}
method Step {n} {
foreach {num den} $fracs { if {$n % $den} continue return [expr {$n * $num / $den}] } return -code break
}
method Generate {n} {
yield [info coroutine] while 1 { yield $n set n [my Step $n] } return -code break
}
}
set ft [Fractran new {
17/91 78/85 19/51 23/38 29/33 77/29 95/23 77/19 1/17 11/13 13/11 15/14 15/2 55/1
}] puts [$ft execute 2]</lang>
- Output:
2 15 825 725 1925 2275 425 390 330 290 770 910 170 156 132
You can just collect powers of 2 by monkey-patching in something like this: <lang tcl>oo::objdefine $ft method pow2 {n} {
set co [coroutine [incr nco] my Generate 2]
set pows {}
while {[llength $pows] < $n} {
set item [$co] if {($item & ($item-1)) == 0} { lappend pows $item }
} return $pows
} puts [$ft pow2 10]</lang> Which will then produce this additional output:
2 4 8 32 128 2048 8192 131072 524288 8388608