Finding the Particular digit of Pi using TakeWhile

TakeWhile[First[RealDigits[Pi, 10, 100]], # != 7 &]


This is used to calculate the first occurrence of 7 but how to get the 20th occurrence of 7.

2 Answers
2

In three steps so that it is easier to understand what's going on:

First[RealDigits[Pi, 10, 1000]] // Short
Position[%, 7][[20, 1]]
%%[[1 ;; % - 1]]


TakeWhile

ClearAll[digitsUpToMthK]
digitsUpToMthK[mth_, k_, n_] := Module[t = 0,
TakeWhile[First[RealDigits[Pi, 10, n]], Or[# != k, (++t) < mth] &]]


Examples:

digitsUpToMthK[3, 7, 10000]


3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9

Length @ digitsUpToMthK[20, 7, 1000]


301

Short @ digitsUpToMthK[20, 7, 1000]


3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8,

<< 230 >>,

4, 8, 6, 1, 0, 4, 5, 4, 3, 2, 6, 6, 4, 8, 2, 1, 3, 3, 9, 3, 6, 0, 7, 2, 6, 0, 2, 4, 9, 1, 4, 1, 2, 7, 3

If you need the position of $m$th occurence of a given digit, you can use LengthWhile:

LengthWhile

ClearAll[posOfMthK]
posOfMthK[mth_, k_, n_] := Module[t = 0,
1 + LengthWhile[First[RealDigits[Pi, 10, n]], Or[# != k, (++t) < mth] &]]


Examples:

posOfMthK[20, 7, 100000]


302

posOfMthK[100, 3, 100000]


937

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