### QB64: Wondrous Numbers.

Posted:

**Tue Jul 23, 2013 8:27 pm**This is not a question, just an observation with a number game/function.

If you have read Godel Escher Bach, you would know what a Wondrous number is.

This site defines it nicely

http://mathforum.org/library/drmath/view/57184.html

Now the site thinks you need pencil and paper to determine if a number is one or not. I have a computer. I'll make it do the work.

Here's the program I wrote back a few years ago. (Pardon my lack of new QB64 commands, we have a better basic now)

Note the two functions. One is recursive, one is not. I'd be careful with the recursive one, you don't know how many steps it will take and the stack is vulnerable.

Anyone here into strange or useless functions?

Jack T.

If you have read Godel Escher Bach, you would know what a Wondrous number is.

This site defines it nicely

http://mathforum.org/library/drmath/view/57184.html

*Start with an arbitrary natural number (integer greater than zero). If the number is even, divide it by 2. If it is odd, multiply by 3 and add 1. Repeat until you come out with 1. A number is wondrous if and only if it eventually reaches 1 through this process*Now the site thinks you need pencil and paper to determine if a number is one or not. I have a computer. I'll make it do the work.

Here's the program I wrote back a few years ago. (Pardon my lack of new QB64 commands, we have a better basic now)

Code: Select all

```
DECLARE FUNCTION get.a.key$ ()
DECLARE SUB pause ()
DECLARE FUNCTION w2! (a!)
DECLARE FUNCTION wonderous! (a!)
CLS
PRINT "Wonderous numbers - what ones are?"
PRINT
qq = 1
WHILE 0 = 0
FOR a = 1 TO 40
r = INT(RND * 1000000)
PRINT "W("; r; ") = "; w2(r)
NEXT
pause
WEND
FOR t = 1 TO 10000
FOR a = qq TO qq + 39
PRINT "W("; a; ") = "; w2(a)
NEXT
pause
qq = qq + 40
NEXT
FUNCTION get.a.key$
temp$ = INKEY$
WHILE temp$ = ""
temp$ = INKEY$
WEND
get.a.key$ = temp$
END FUNCTION
SUB pause
PRINT
PRINT "<press any key>"
aa$ = get.a.key$
END SUB
FUNCTION w2 (a)
'inputs a, returns 1 if wonderous, not recursive
a1 = a 'temp var to use
WHILE a1 > 1
IF a1 = 1 THEN w2 = 1: EXIT FUNCTION
IF a1 < 1 OR INT(a1) <> a1 THEN PRINT "ERROR "; a: STOP
IF a1 / 2 = INT(a1 / 2) THEN
a1 = a1 / 2
ELSE
a1 = 3 * a1 + 1
END IF
'PRINT a1;
WEND
w2 = a1
END FUNCTION
FUNCTION wonderous (a)
IF a = 1 THEN wonderous = 1: EXIT FUNCTION
IF a < 1 THEN PRINT "ERROR "; a: STOP
IF a / 2 = INT(a / 2) THEN
'PRINT "even": STOP
'PRINT a / 2
wonderous = wonderous(a / 2)
ELSE
'PRINT "odd": STOP
wonderous = wonderous(3 * a + 1)
END IF
END FUNCTION
```

Anyone here into strange or useless functions?

Jack T.