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 >> >> >> >

**References**:**Seaching in Pi a sequence. Looking for a faster method***From:*Guillermo Sanchez <guillermo.sanchez@hotmail.com>