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Seaching in Pi a sequence. Looking for a faster method

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  Seaching in Pi a sequence. Looking for a faster method Guillermo Sanchez <guillermo.sanchez@hotmail.com> - 2011-06-10 10:38 +0000
    Re: Seaching in Pi a sequence. Looking for a faster method rafapa <rafapa@us.es> - 2011-06-12 09:07 +0000

#3062 — Seaching in Pi a sequence. Looking for a faster method

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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#3080

On Jun 10, 12:38 pm, Guillermo Sanchez <guillermo.sanc...@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

What about

piesimoR[n_, m_String] := First /@
StringPosition[StringDrop[ToString[N[Pi, n]], 2], m]
piesimoR[10^7, "9999999"]//Timing

{4.04938, {1722776, 3389380, 4313727, 5466169}}

The original gave

piesimo[10^7, 9, 7]

{9.56055, {1722776, 3389380, 4313727, 5466169}}

If you intend to search several sequences it's better to save the
stringfied pi

pistring = StringDrop[ToString[N[Pi, 10^7]], 2];
piesimoS[m_String] := First /@ StringPosition[pistring, m]

piesimoS["9999999"]//Timing

{0.203969, {1722776, 3389380, 4313727, 5466169}}

piesimoS["1234567"]//Timing

{0.203969, {9470344}}


Rafael

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