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

*To*: mathgroup at smc.vnet.net*Subject*: [mg119584] Re: Seaching in Pi a sequence. Looking for a faster method*From*: Anthony Hodsdon <ajhodsd at hotmail.com>*Date*: Sat, 11 Jun 2011 03:58:30 -0400 (EDT)*References*: <201106101038.GAA19889@smc.vnet.net>

This sounds like a job for string search: piesimo2[n_, m_, r_] := Transpose[ StringPosition[StringDrop[ToString[N[Pi, n]], 2], ToString[m*(10^r - 1)/9]]][[1]] In[44]:= piesimo2[10^7, 9, 7] // Timing Out[44]= {19.063, {1722776, 3389380, 4313727, 5466169}} Not bad, considering "stringifying" pi to begin with seems to take most of the time: In[49]:= ToString[N[Pi, 10^7]]; // Timing Out[49]= {18.19, Null} Mathematica can do the actual search very quickly using a linear time (in terms of n+r) algorithm (see, for instance, http://en.wikipedia.org/wiki/String_searching_algorithm). --Anthony -----Original Message----- From: Guillermo Sanchez [mailto:guillermo.sanchez at hotmail.com] Sent: Friday, June 10, 2011 3:38 AM To: mathgroup at smc.vnet.net Subject: [mg119584] 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

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