4 ms·
Assuming that pi has an infinite number of digits, then the answer to "What is the longest known sequence that repeats in Pi?" is "The longest known sequence of
by 34679 2y ago
Assuming that pi has an infinite number of digits, then the answer to "What is the longest known sequence that repeats in Pi?" is "The longest known sequence of Pi".
- sponaugle 2y agoHa! Yea, that is true.. now if we only had a printout of it!
- Misdicorl 2y agoThis isn't true as you can build an infinite sequence that never repeats. An example sequence in binary is (the number of 0s between each 1 increases by 1 every time) 01001000100001...
- poizan42 2y agoExactly. A number with the property that every sequence occurs is called a rich or disjunctive number - a number can be rich in s specific bases or rich for all bases we don't know whether pi is any if that. A number where every sequence occurs equally often (scaled to the length of the sequence) is called a normal number, which is an even stronger property.
- sponaugle 2y agoWhile Pi is not proven to be a disjunctive number, nor the stronger condition of being normal, it is generally believed to be normal. That being said we don't have a proof of Pi being normal, nor disjunctive. I am not familiar with how a proof of that would be constructed, as clearly numerical or computational measurements could never be conclusive.
- jfoutz 2y agoStarting from the fourth digit, 01000100 But maybe I don’t understand your example
- Misdicorl 2y agoYou didn't understand the original claim which is that because Pi has an infinite decimal representation, every subsequence of it has a repeat
- jfoutz 2y agoAhh, you’re saying something like every sequence containing at least 2 ones, does not repeat. There may be some long repeats, but not all sequences repeat. Thanks!
- 34679 2y agoYour example is governed by an arbitrary rule of your choosing. Pi is not.
- nimih 2y agoThat assumption is empirically supported, but is, as of now, conjectural and unproven. In fact, our ability to prove facts about the distribution of digits in pi is so weak that we can't even rule out statements such as "after a certain point, all digits of pi represented in base 10 are either 0 or 1."
- markusde 2y agoThe longest sequence of digits that eventually repeat (as defined in the article) is unboundedly large for any infinite sequence of digits, not just pi! Using the pigeonhole principle, there must be at least one length N repeating string in the first N(N!+1) characters of any string.