Re: Numbers and their reversals

*To*: mathgroup at smc.vnet.net*Subject*: [mg53699] Re: [mg53687] Numbers and their reversals*From*: DrBob <drbob at bigfoot.com>*Date*: Mon, 24 Jan 2005 03:37:20 -0500 (EST)*References*: <200501230702.CAA11076@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Here's a modification to allow palindromes optionally, and an "explain" routine that shows how a number factors in this way (if it does): Clear[omariQ,omariD,explain] reverse=FromDigits@Reverse@IntegerDigits@#&; commonDivisors=Rest@Divisors@GCD[#,reverse@#]&; omariQ[n_Integer,k_Integer, palindromes_:False]:=(palindromes||n!=reverse@n)&&IntegerQ[n/k]&& k reverse[n/k]\[Equal]reverse@n omariD[n_Integer,palindromes_:False]:=Select[commonDivisors@n,omariQ[n,#,\ palindromes]&] omariQ[n_Integer,palindromes_:False]:=Length@omariD[n,palindromes]>0 explain[n_,palindromes_: False]/;omariQ[n,palindromes]:=Module[{o=omariD[n,palindromes],tmp}, Print["The omari divisors of n = ",n," are o = ",o]; Print["n/o : ",tmp=n/o]; Print["reverse/@(n/o) : ",tmp=reverse/@tmp]; Print["o reverse/@(n/o) : ",tmp=o tmp]; ] explain[__]:=Null explain[17*242] (no output) explain[17*242, True] "The omari divisors of n = "4114" are o = "{17, 34, 187, 374, 2057, 4114} "n/o : "{242, 121, 22, 11, 2, 1} "reverse/@(n/o) : "{242, 121, 22, 11, 2, 1} "o reverse/@(n/o) : "{4114, 4114, 4114, 4114, 4114, 4114} explain[627172] "The omari divisors of n = "627172" are o = "{91} "n/o : "{6892} "reverse/@(n/o) : "{2986} "o reverse/@(n/o) : "{271726} Bobby On Sun, 23 Jan 2005 02:02:17 -0500 (EST), F. omari <towtoo2002 at yahoo.com> wrote: > > 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 > > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Numbers and their reversals***From:*"F. omari" <towtoo2002@yahoo.com>