Re: Random numbers according to a rule / function

• To: mathgroup at smc.vnet.net
• Subject: [mg68955] Re: [mg68933] Random numbers according to a rule / function
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 25 Aug 2006 05:35:11 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```conditionalRandom[test_Function, type_:Integer, range_]:=
Module[{r},
While[Not[test[r=Random[type,range]]]];
r];

test1=(Mod[#,13]==0&&Mod[#,19]==0)&;

a=conditionalRandom[test1,{100,1000}]

494

test1[a]

True

test2=PrimeQ[#]&&Total[IntegerDigits[#]]==10&;

b=conditionalRandom[test2,{1,10000}]

9001

test2[b]

True

Bob Hanlon

---- bd satish <bdsatish at gmail.com> wrote:
> Hi buddies ,
>
>                I want to write a module / program that generates random
> numbers according to some rule (or function).
>
> Say , "A number that is divisible by 13 & 19" or "A prime number whose sum
> of digits is exactly 10" , etc.
>
> Let me call this module as RandomRule[ f ].   Everytime I evaluate this
> function , I must get a number 'x' such that f [x] is True.
>
> For different invokes , RandomRule[ f ] must give different values.  There
> are no restrictions on the function ' f ' .
>
> For simplicity, let ' x '  be an integer.
>
>             This is what I tried :
>
> "A number that is divisible by 13 and 19"
>
>      I put the command
>
>               (Mod [ # , 14 ] == 0  &&  Mod[ # , 19 ] ==0  )&
> Random[Integer,{100,1000}]
>
>  in a Do loop until the above statement returns True. And returned the value
> of Random[Integer,{100,1000}]
> that made this statement True.
>
>  My problem is , how can I generalize this to include ANY function ' f ' ?
>

```

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