Re: Seaching in Pi a sequence. Looking for a faster method

• To: mathgroup at smc.vnet.net
• Subject: [mg119590] Re: Seaching in Pi a sequence. Looking for a faster method
• From: Phil J Taylor <xptaylor at gmail.com>
• Date: Sat, 11 Jun 2011 03:59:35 -0400 (EDT)
• References: <201106101038.GAA19889@smc.vnet.net>

```I made a couple of minor modifications after noticing problems with
Feynman's Point and patterns that begin with zeros. I'm not sure why, but
searching for 9999998 didn't return correct results until I added the
_Integer qualifier to the start and end rules. I haven't fixed the leading
zeros problem. Just put the pattern in quotes.

(* loosely validated at http://www.angio.net/pi/bigpi.cgi *)

piStringSearch[n_, s_, c_] :=
Module[{piString = ToString[N[Pi, n]]},
StringPosition[piString, ToString[s],
c] /. {start_Integer, end_Integer} :> start - 2]

piStringSearch[10^5, "00000", 100]

{17534}

On Fri, Jun 10, 2011 at 2:45 PM, Phil J Taylor <xptaylor at gmail.com> wrote:

> This works well for me ... it's about 3x faster than piesimo on my machine
> and I can search for any sequence.
> The final argument c is the number of matches that you are interested in
> seeing.
>
> piStringSearch[n_, s_, c_] :=
>  Module[{a}, a = ToString[N[Pi, n]];
>   StringPosition[a, ToString[s], c] /. {start_, end_} :> start - 2]
>
> piStringSearch[10^7, 9999999, 100]
>
> {1722776, 3389380, 4313727, 5466169}
>
> On Fri, Jun 10, 2011 at 6:38 AM, Guillermo Sanchez <
> guillermo.sanchez at hotmail.com> wrote:
>
>> Dear Group
>>
>> I have developed this function
>>
>> piesimo[n_, m_, r_] := Module[{a}, a = Split[RealDigits[Pi - 3, 10, n]
>> [[1]]]; Part[Accumulate[Length /@ a], Flatten[Position[a, Table[m,
>> {r}]]] - 1] + 1]
>>
>> n is the digits of Pi, after 3, where to search a sequence of m digit
>> r times consecutives.
>> For instance:
>>
>> piesimo[10^7, 9, 7]
>>
>> Gives that the sequence 9999999 happens in positions:
>>
>> {1722776, 3389380, 4313727, 5466169}
>>
>> I know that in this group I will find  faster methods. Any idea?
>>
>> Guillermo
>>
>>
>>
>

```

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