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

• To: mathgroup at smc.vnet.net
• Subject: [mg119600] Re: Seaching in Pi a sequence. Looking for a faster method
• From: Phil J Taylor <xptaylor at gmail.com>
• Date: Sun, 12 Jun 2011 05:06:08 -0400 (EDT)
• References: <201106101038.GAA19889@smc.vnet.net>

```That works great, thanks! I'm new with Mathematica ... still a lot to learn!

piStringSearch[n_, s_, c_] :=
Replace[StringPosition[ToString@N[Pi, n], ToString@s,
c], {start_, end_} :> start - 2, 1]

The leading zero problem appears when you use numbers without the quotes
like this:

piStringSearch[ 10^3, 09999, 100]
{762, 763, 764}

It's not correct that way ... the leading zero is dropped by ToString which
is ok. Just use quotes like you did.

piStringSearch[ 10^3, "09999", 100]
{}

On Sat, Jun 11, 2011 at 2:57 PM, DrMajorBob <btreat1 at austin.rr.com> wrote:

> searching for 9999998 didn't return correct results until I added the
>> _Integer qualifier to the start and end rules.
>>
>
> That's because exactly two matches were found:
>
> piStringSearch[n_, s_, c_] :=
>  StringPosition[ToString@N[Pi, n], ToString@s, c]
>
> piStringSearch[10^7, "9999998", 100]
> % /. {start_, end_} :> start - 2
>
> {{764, 770}, {3062883, 3062889}}
>
> {762, 768}
>
>
> piStringSearch[n_, s_, c_] := -2 +
>  StringPosition[ToString@N[Pi, n], ToString@s, c][[All, 1]]
>
> piStringSearch[10^7, "9999998", 100]
>
> {762, 3062881}
>
> That still fails if NO matches are found, so this is safer than either
> method above:
>
> Clear[piStringSearch]
> piStringSearch[n_, s_, c_] :=
>  Replace[StringPosition[ToString@N[Pi, n], ToString@s,
>   c], {start_, end_} :> start - 2, 1]
>
> piStringSearch[10^7, "9999998", 100]
>
> {762, 3062881}
>
>
> piStringSearch[10^7, "9999999", 100]
>
> {1722776, 3389380, 4313727, 5466169}
>
> Table[piStringSearch[10^7, "000000" <> ToString@i, 100], {i, 0, 9}]
>
> {{3794572}, {3794573}, {2609392,
>  7257528}, {}, {}, {1699927}, {}, {}, {2328783}, {}}
>
> piStringSearch[10^7, "000000", 100]
>
> {1699927, 2328783, 2609392, 3794572, 3794573, 7257528}
>
> What is the "leading zeros problem"?
>
> Bobby
>
>
> On Sat, 11 Jun 2011 02:59:35 -0500, Phil J Taylor <xptaylor at gmail.com>
> wrote:
>
>  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
>>>>
>>>>
>>>>
>>>>
>>>
>
> --
> DrMajorBob at yahoo.com
>

```

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