Finding the Particular digit of Pi using TakeWhile

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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.

list-manipulation

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edited Sep 2 at 18:34

AccidentalFourierTransform

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asked Sep 2 at 18:23

Bignya ranjan Pathi

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up vote
2
down vote

favorite

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.

list-manipulation

share|improve this question

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

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.

list-manipulation

share|improve this question

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

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.

list-manipulation

share|improve this question

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

share|improve this question

share|improve this question

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

edited Sep 2 at 18:34

AccidentalFourierTransform

4,398838

4,398838

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

asked Sep 2 at 18:23

Bignya ranjan Pathi

254

254

add a comment | 

add a comment | 

2 Answers
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4
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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]]

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answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

add a comment | 

up vote
3
down vote

... using 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:

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

share|improve this answer

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
4
down vote

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]]

share|improve this answer

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

add a comment | 

up vote
4
down vote

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]]

share|improve this answer

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

add a comment | 

up vote
4
down vote

up vote
4
down vote

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]]

share|improve this answer

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

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]]

share|improve this answer

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

share|improve this answer

share|improve this answer

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

answered Sep 2 at 18:37

AccidentalFourierTransform

4,398838

4,398838

add a comment | 

add a comment | 

up vote
3
down vote

... using 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:

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

share|improve this answer

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

add a comment | 

up vote
3
down vote

... using 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:

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

share|improve this answer

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

add a comment | 

up vote
3
down vote

up vote
3
down vote

... using 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:

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

share|improve this answer

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

... using 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:

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

share|improve this answer

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

share|improve this answer

share|improve this answer

edited Sep 2 at 20:02

edited Sep 2 at 20:02

edited Sep 2 at 20:02

answered Sep 2 at 19:55

kglr

159k8183382

answered Sep 2 at 19:55

kglr

159k8183382

answered Sep 2 at 19:55

kglr

159k8183382

159k8183382

add a comment | 

add a comment | 

 

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