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Important pi question (when these numbers will reoccur)

by 9I.
Tags: important, numbers, reoccur
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9I.
#1
Jul25-14, 02:05 PM
P: 3
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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micromass
#2
Jul25-14, 02:19 PM
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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
[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.
9I.
#3
Jul25-14, 10:19 PM
P: 3
i never referenced it to the volume of universe anyway.

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


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