Re: Numbers and their reversals

• To: mathgroup at smc.vnet.net
• Subject: [mg53705] Re: [mg53687] Numbers and their reversals
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 24 Jan 2005 03:37:26 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```reverseDigits[n_Integer] :=
FromDigits[Reverse[IntegerDigits[n]]];

f[m_Integer, maxRange_Integer:3000] :=
Select[Range[maxRange],
reverseDigits[#]*m==reverseDigits[#*m]&];

f[17]

{242,484,2420,2442,2662,2684}

f[17,5000]

{242,484,2420,2442,2662,2684,4840,4862}

Length[f[91]]

746

Bob Hanlon

>
> From: "F. omari" <towtoo2002 at yahoo.com>
To: mathgroup at smc.vnet.net
> Date: 2005/01/23 Sun AM 02:02:17 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg53705] [mg53687] Numbers and their reversals
>
>
> 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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