/* gnubc program: cloitre */

"
			The Benoit Cloitre CONJECTURE:







if cloitre(y) is typed in, the iterates

y, t(y), t(t(y)),... of the Benoit Cloitre function t(x) are printed

and the number of steps taken to reach one of 0, -1, -4, -19

is recorded. Benoit Cloitre conjectured in an email to Jeff Lagarias

 dated July 19, 2011, that every trajectory starting from 

a positive integer will eventually reach 0.

Experimentally it is certain that any trajectory starting from a 

negative integer will evevntually reach one of -1, -4 or -19.
"

/* the Benoit Cloitre function */

/*  the least non-negative remainder when an integer a is divided by a positive
integer b */

/* a%b=m(a,b) if a>=0 or a<0 and b divides a */
/* a%b=m(a,b)-b if a<0, b>0, a not divisible by b */

define mod(a,b){
	auto c
	c=a%b
	if(a>=0) return(c)
	if(c==0) return(0)
        return(c+b)	
}

define t(x){
auto r
   r=mod(x,3)
   if(r==0) return(2*x/3)
   if(r==1) return((x-1)/3)
   return(5*x+3)
}

define cloitre(y){
	auto i,x
	x=y
		for(i=0;i>=0;i++){
	
                        print "i=",i,":",x,"\n"
			if(x==0 || x == -1 || x == -4 || x == -19){
				print "starting number = ",y,","
				print "the number of iterations taken to reach ",x, " is "
				return(i)
			}
			x=t(x)
		}
}