/* filename: 4_branch */

"




			A 4-branch conjecture.






If s(y) is typed in, the iterates y, t(y), t(t(y)),... 

of the 4-branched function t(x) below are printed and the number of steps

taken to reach one of 0, -3, 2, 3, 6,-18, -46, -122, -330, -117, -137

-186, -750, -261, -333, 5127 is recorded. 

(It seems certain that every trajectory  will end in one of these numbers.)

Type qu to exit the program.
"
/*  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 m(a,b){
	auto c
	c=a%b
	if(a>=0) return(c)
	if(c==0) return(0)
        return(c+b)	
}

/* int(a,b)=integer part of a/b, a, b integers, b != 0 */

define int(a,b){
	if(b<0){
	a= -a
	b= -b
	}
	return((a-m(a,b))/b)
}

/* the 4-branched function */

define t(x){
auto y
     y=m(x,4)
	if(y==0) return(x/4)
	if(y==1) return(int(3*x,4))
	if(y==2) return(int(5*x,4))
	return(int(17*x,4))
}

define s(y){
	auto i,x
	x=y
		for(i=0;i>=0;i++){
			if(x==0){
				"starting value = ";y
				"the number of iterations taken to reach 0 is "
				return(i)
			}
			if(x==-3){
				"starting value = ";y
				"the number of iterations taken to reach -3 is "
				return(i)
			}
			if(x==2){
				"starting value = ";y
				"the number of iterations taken to reach 2 is "
				return(i)
			}
			if(x==3){
				"starting value = ";y
				"the number of iterations taken to reach 3 is "
				return(i)
			}
			if(x==6){
				"starting value = ";y
				"the number of iterations taken to reach 6 is "
				return(i)
			}
			if(x==-18){
				"starting value = ";y
				"the number of iterations taken to reach -18 is "
				return(i)
			}
			if(x == -46){
				"starting value = ";y
				"the number of iterations taken to reach -46 is "
				return(i)
			}
			if(x == -122){
				"starting value = ";y
				"the number of iterations taken to reach -122 is "
				return(i)
			}
			if(x == -330){
				"starting value = ";y
				"the number of iterations taken to reach -330 is "
				return(i)
			}
			if(x == -117){
				"starting value = ";y
				"the number of iterations taken to reach -117 is "
				return(i)
			}
			if(x == -137){
				"starting value = ";y
				"the number of iterations taken to reach -137 is "
				return(i)
			}
			if(x == -186){
				"starting value = ";y
				"the number of iterations taken to reach -186 is "
				return(i)
			}
			if(x == -750){
				"starting value = ";y
				"the number of iterations taken to reach -750 is "
				return(i)
			}
			if(x == -261){
				"starting value = ";y
				"the number of iterations taken to reach -261 is "
				return(i)
			}
			if(x == -333){
				"starting value = ";y
				"the number of iterations taken to reach -333 is "
				return(i)
			}
			if(x == 5127){
				"starting value = ";y
				"the number of iterations taken to reach 5127 is "
				return(i)
			}
			(x=t(x))
		}
}