Important pi question (when these numbers will reoccur)

In summary: Graham's number, but it's unlikely that it will ever be found again due to the vast number of digits in pi. In summary, the first 9 digits of pi (141592653) have a digital root of 9, and this same sequence occurs at the 427238911 place in the pi chain. It is a special occurrence and the question remains of when it will happen again, if ever. It is suspected that this sequence is somewhere in Graham's number, but it is unlikely to be found again due to the vast number of digits in pi.
  • #1
9I.
3
0
after it was found out that the first 9 pi digits 141592653 result in the end sum of 9, i searched for its iteration in the large digit chain of pi. after scanning stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt it was found that .141592653 occurs at the 427238911 place and ends on the 427238920.

not only is 9 my favorite number for mathematical reasons (and non mathematical) but its also a coincidence that the first 9 pi digits end on the digital root of 9, making it the first number which has the same digit sum as also same digital root

thus we can leave it at that it qualifies to be seen as a special occurence in the digital pi chain. the great pi question is on which pi digit do the 427,238,911 numbers start to iterate again. this exact chain of pi digits. it happened once in 427 million, and when will it happen again, all these 427 million as one piece?
 
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  • #2
We don't even know if it will happen again. But if ##\pi## is a normal number, meaning that all finite sequences are equally likely (which has not been proven yet, but is suspected strongly to be the case), then for a given sequence of ##n## numbers to show up, you will have to go approximately
[tex]\frac{10}{9}(10^n - 1)\approx 10^n[/tex]

digits far in the sequence. So if you want to see the 427,238,911 again, you will have to wait approximately ##10^{427238911}## digits. In comparison, the number of particles in the observable universe is approximately ##10^{80}##, so you'll probably never be able to find this sequence in ##\pi## since there's not enough space to store the digits.
 
  • #3
i never referenced it to the volume of universe anyway.

so that means this number is somewhere in g1(grahams)?
 
  • #4
9I. said:
after it was found out that the first 9 pi digits 141592653 result in the end sum of 9, i searched for its iteration in the large digit chain of pi. after scanning stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt it was found that .141592653 occurs at the 427238911 place and ends on the 427238920.

not only is 9 my favorite number for mathematical reasons (and non mathematical) but its also a coincidence that the first 9 pi digits end on the digital root of 9, making it the first number which has the same digit sum as also same digital root

thus we can leave it at that it qualifies to be seen as a special occurence in the digital pi chain. the great pi question is on which pi digit do the 427,238,911 numbers start to iterate again. this exact chain of pi digits. it happened once in 427 million, and when will it happen again, all these 427 million as one piece?
If you digitally root a radian, you will get the same thing. M.
 

1. When will the numbers in pi start repeating?

The numbers in pi will never start repeating. Pi is an irrational number, which means it has an infinite number of digits with no repeating pattern.

2. How many digits of pi are known?

As of 2021, the most accurate calculation of pi has been done to 62.8 trillion digits. However, for practical purposes, only about 39 digits of pi are needed for most calculations.

3. Will the numbers in pi eventually end or repeat?

No, the numbers in pi will never end or repeat. As mentioned earlier, pi is an irrational number and has an infinite number of digits with no repeating pattern.

4. Are there any patterns in the digits of pi?

Despite the fact that pi is an irrational number, there have been attempts to find patterns in its digits. However, no repeating pattern has been found and it is believed that there is no pattern in the digits of pi.

5. Can computers calculate pi accurately?

Computers can calculate pi to a very high degree of accuracy, but due to its infinite nature, it is impossible to calculate pi completely accurately. The more digits that are calculated, the longer it takes and the more memory it requires.

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