$n$ such that the digits immediately after the decimal point of $pi^n$ give $n$ again
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I was doing something with value of $pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator:
$$ pi^4 = 97.40909103400243723644033268870511124972758567268542169146... $$
as we can see the power of $pi$ is $4$ and on right hand side the number after decimal place is also $4$.
Now a question arise in my mind:
"Is there any value also exist which can show the below relation as $4$ did?"
$$ pi^n = ....ABCD.nPQRST....... $$ ( where n is the number after decimal which can be of any digits)
I still don't get any clue.Any hint or solution will helpful for me. Thanks.
number-theory irrational-numbers pattern-recognition
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up vote
-2
down vote
favorite
I was doing something with value of $pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator:
$$ pi^4 = 97.40909103400243723644033268870511124972758567268542169146... $$
as we can see the power of $pi$ is $4$ and on right hand side the number after decimal place is also $4$.
Now a question arise in my mind:
"Is there any value also exist which can show the below relation as $4$ did?"
$$ pi^n = ....ABCD.nPQRST....... $$ ( where n is the number after decimal which can be of any digits)
I still don't get any clue.Any hint or solution will helpful for me. Thanks.
number-theory irrational-numbers pattern-recognition
1
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I was doing something with value of $pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator:
$$ pi^4 = 97.40909103400243723644033268870511124972758567268542169146... $$
as we can see the power of $pi$ is $4$ and on right hand side the number after decimal place is also $4$.
Now a question arise in my mind:
"Is there any value also exist which can show the below relation as $4$ did?"
$$ pi^n = ....ABCD.nPQRST....... $$ ( where n is the number after decimal which can be of any digits)
I still don't get any clue.Any hint or solution will helpful for me. Thanks.
number-theory irrational-numbers pattern-recognition
I was doing something with value of $pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator:
$$ pi^4 = 97.40909103400243723644033268870511124972758567268542169146... $$
as we can see the power of $pi$ is $4$ and on right hand side the number after decimal place is also $4$.
Now a question arise in my mind:
"Is there any value also exist which can show the below relation as $4$ did?"
$$ pi^n = ....ABCD.nPQRST....... $$ ( where n is the number after decimal which can be of any digits)
I still don't get any clue.Any hint or solution will helpful for me. Thanks.
number-theory irrational-numbers pattern-recognition
edited Aug 20 at 11:20
Blue
43.8k868141
43.8k868141
asked Aug 20 at 11:06
Adarsh Kumar
519
519
1
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23
add a comment |Â
1
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23
1
1
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
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accepted
Next ones are $75$, $9,424$ and $12,669$. I do not see any pattern.
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Next ones are $75$, $9,424$ and $12,669$. I do not see any pattern.
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
add a comment |Â
up vote
2
down vote
accepted
Next ones are $75$, $9,424$ and $12,669$. I do not see any pattern.
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Next ones are $75$, $9,424$ and $12,669$. I do not see any pattern.
Next ones are $75$, $9,424$ and $12,669$. I do not see any pattern.
edited Aug 20 at 14:45
answered Aug 20 at 14:38
Julián Aguirre
65.2k23894
65.2k23894
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
add a comment |Â
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
Sir did you use any program to calculate these values?
â Adarsh Kumar
Aug 20 at 14:40
1
1
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Yes, Mathematica.
â Julián Aguirre
Aug 20 at 14:40
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Ok thanks a lot for giving your time for my question.
â Adarsh Kumar
Aug 20 at 14:41
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time.
â Adarsh Kumar
Aug 20 at 15:02
add a comment |Â
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1
$n=0$ and $n=1$ work!
â Blue
Aug 20 at 11:21
Yes but I not getting higher values so that I can do work on making a general formula for this property
â Adarsh Kumar
Aug 20 at 11:23