       Re: Numbers and their reversals

• To: mathgroup at smc.vnet.net
• Subject: [mg53706] Re: Numbers and their reversals
• From: "Scout" <user at domain.com>
• Date: Mon, 24 Jan 2005 03:37:27 -0500 (EST)
• References: <csvia0\$asu\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Let
n * k = z
Rev(n) * k = Rev(z)

--------------------------------------------------------------
ris={}; (* list of results in the form {number n, constant k} *)

Do[

If[Mod[n,10]¹ 0, (* no closing zeroes *)

nr=FromDigits[Reverse[IntegerDigits[n]]];

Do[

z=k*n;

zr=FromDigits[Reverse[IntegerDigits[z]]];

If[zr¹ z, (* no palindromes *)

If[nr*kSzr,AppendTo[ris,{n,k}]]

],{k,2,99} (* first and last k *)

]

],{n,11,101} (* first and last n *)

];

Print[ris];

-----------------------------------------------------

That's all.

~Scout~

"F. omari"
>
> i want to investigate the following two equations:
> a * const = z
> a_Reversed * const = z_Reversed
> where a, z, and their reversed form and const are all positive integers
> ie such that:
> 2684 * 17 = 45628
> 4862 * 17 = 82654
> 2986 * 91 = 271726
> 6892 * 91 = 627172
> it happened that many multipliers of 91 have such a property.
> while the multipliers of 17 have only 5 cases in the interval of 1 to 3000
> the following code will investigate the multipliers of 17, to investigate
> another number just replace 17. and you may increase the interval of
> investigation. i am sure that my code is an old fashion one, please any
> other ideas about a more functional code.
> a = Table[i, {i, 1, 3000}]; zR = ""; aR = 0; z = "";
> Do[aR = ToExpression[StringReverse[ToString[a[[i]]]]];
>        z = ToString[a[[i]]*17];
>       zR = StringReverse[ToString[aR*17]];
>       If[zR == z, Print[a[[i]]]], {i, 1, 3000}]
>
> 242
> 484
> 2442
> 2662
> 2684
> regards
>
>

```

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