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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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