Important pi question (when these numbers will reoccur)

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Discussion Overview

The discussion revolves around the occurrence of the first nine digits of pi (3.141592653) and their significance, particularly focusing on the digital root and the potential for this sequence to reappear within the digits of pi. Participants explore the implications of pi being a normal number and the likelihood of finding this specific sequence again.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the first nine digits of pi sum to 9 and questions when this sequence will reoccur in the digits of pi, having found its first occurrence at position 427,238,911.
  • Another participant suggests that if pi is a normal number, the likelihood of finding any specific sequence, such as the one mentioned, would require an immense number of digits, potentially beyond practical limits.
  • A different participant questions the relevance of the universe's size to the occurrence of the sequence in pi.
  • One participant reiterates their initial findings about the sequence and its significance, emphasizing the digital root aspect.
  • A final comment introduces the idea of digitally rooting a radian, suggesting a connection to the discussion but without further elaboration.

Areas of Agreement / Disagreement

Participants express differing views on the likelihood of the sequence reappearing in pi, with some suggesting it may never occur again due to the vast number of digits required, while others focus on the significance of the sequence itself without consensus on its future occurrence.

Contextual Notes

The discussion includes assumptions about the nature of pi and its digits, particularly the unproven hypothesis of pi being a normal number, which affects the claims about the occurrence of sequences within its digits.

9I.
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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 occurrence 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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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
\frac{10}{9}(10^n - 1)\approx 10^n

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.
 
i never referenced it to the volume of universe anyway.

so that means this number is somewhere in g1(grahams)?
 
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 occurrence 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.
 

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