Re: Number-Theory :: All-Digit Perfect Squares

*To*: mathgroup at smc.vnet.net*Subject*: [mg64281] Re: Number-Theory :: All-Digit Perfect Squares*From*: "Scout" <Scout at nodomain.com>*Date*: Thu, 9 Feb 2006 02:44:48 -0500 (EST)*References*: <dscd0p$pcm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"bd satish" <bdsatish at gmail.com> > Hi buddies, > > > I set out to write a code that generates > nine-digit > perfect square numbers , with each of the digits 1,2,3,...9 occuring only > once > in a given number. An example is 139854276 = 11826^2 . Obviuously , all > such numbers must lie in the interval [123456789 , 987654321] . Since > 11111^2 < 123456789 and 31427^2 > 987654321 , all the square numbers must > have their square-roots > in the interval (11111,31427) . > > I need suggetions from you guys to help me improve the code > or > to make it better or > shorter. > > The logic I used is this: > > (a). Generate all the squares of integers in the range [11111,31427] > > (b). Seperate the numbers into digits (using the command IntegerDigits[ ] > ) > > (c). Check , how many (or which and all) numbers in this list have each > of the digits 1,2,3,...8,9 exactly once. > > (d). Collect all those lists and put them back as numbers (using the > command FromDigits[ ] ) > > > Here is the actual code: > > squares = IntegerDigits[Table[i ^ 2 , { i,11111,31427}]]; > sel = { } ; (* empty-list*) > Do[ > p = squares[[k]]; > logic = > And[MemberQ[p,1],MemberQ[p,2],MemberQ[p,3],MemberQ[p,4],MemberQ[p,5],MemberQ[p,6], > MemberQ[p,7],MemberQ[p,8],MemberQ[p,9] ] ; > > If[TrueQ[logic] , sel = Append[sel,p]] , > {k,1,Length[squares]} > ]; > Map[FromDigits,sel,{1}] > > The code does work perfectly, giving a list of 30 such numbers. > > Will anyone help to to improve the code , if possible ? > > I would like to get rid of MemberQ[..] repeated so often. > > In[1]:= Timing[ FromDigits/@Select[IntegerDigits[#^2]&/@Range[11111,31427],PermutationQ] ] Out[1]= {0.156 Second, {139854276,152843769,157326849,215384976,245893761,254817369, 326597184,361874529,375468129,382945761,385297641,412739856,523814769, 529874361,537219684,549386721,587432169,589324176,597362481,615387249, 627953481,653927184,672935481,697435281,714653289,735982641,743816529, 842973156,847159236,923187456} } In[2]:= Length[%[[2]]] Out[2]= 30 ~Scout~