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Re: A list of numbers without "73"

• To: mathgroup at smc.vnet.net
• Subject: [mg63043] Re: A list of numbers without "73"
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sun, 11 Dec 2005 22:25:17 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <dnee1r$1ep$1@smc.vnet.net> <dngtq5$mvu$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Thomas Schmelzer wrote:
> I forgot to say that S(i) is a list of positive integers with i digits.
> Best,
> Thomas
> 
> "Thomas Schmelzer" <thomas.??? at balliol.ox.ac.uk> schrieb im Newsbeitrag 
> news:dnee1r$1ep$1 at smc.vnet.net...
> 
>>Experts,
>>
>>S(i) should be a list of positive integers without the substring "73".
>>
>>My code seems to be very inefficient. I multiply all numbers with 0 if 
>>they
>>contain "73", sort the new list, make the union (remove double elements) 
>>and
>>delete the first element. Therefore it is necessary to use an if statement
>>in order not to delete the first element of the numbers 1-9. Any more
>>sophisticated ideas?
>>
>>L := Table[k, {k, 1, 9}]
>>
>>S[i_] := S[i] =
>>If[i == 1, L,
>>Delete[Union[
>>Table[k*(1 - Boole[StringMatchQ[ToString[k], "*73*"]]), {k,
>>10^(i - 1), 10^i - 1}]], 1]]
>>
>>
>>
>>Best
>>
>>Thomas
Hi Thomas,

You could try a combination of *DeleteCases* and *IntegerDigits* as in

In[1]:=
s[n_]:=FromDigits/@DeleteCases[IntegerDigits/@Range[10^(n-1),
       10^n-1], {___,7,3,___}]

In[2]:=
s[6]//Short//Timing

Out[2]=
{19.828 Second,{100000,100001,
   100002,100003,100004,100005,100006,100007,100008,\[LeftSkeleton]854551\
\[RightSkeleton],999991,999992,999993,999994,999995,999996,999997,999998,\
999999}}

In[3]:=
Complement[Range[10^5,10^6-1],s[6]]//Short

Out[3]//Short=
{100073,100173,100273,100373,100473,100573,100673,100730,100731,\
\[LeftSkeleton]45413\[RightSkeleton],999734,999735,999736,999737,999738,\
999739,999773,999873,999973}

In[4]:=
$Version

Out[4]=
5.2 for Microsoft Windows (June 20, 2005)

(Tested on a Pentium IV 2.6 GHz, 512 Mo)

Best regards,
/J.M.