Hello, the answer is no. First the Kolakoski sequence (A000002) has a specific binary pattern, see for yourself here : http://plouffe.fr/100%20millions%20de%20valeurs%20Kolakoski.png there are 100 million values of A000002 encoded in a color image (for visibility), as you can see if we compare to an image of let's say 100 million digits (in binary) of Pi : there is no doubt about it : Pi is random, Kolakoski is not, it is bizarre, strange and such, but surely not the same as a pure random sequence. Some people I know said me once that this sequence will turn you crazy (la suite qui rend fou). Best regards, bonne soirée. Simon Plouffe Le 2019-10-24 à 18:48, Éric Angelini a écrit :
Hello Math-Fun, I read here https://bit.ly/2NmIOnh that 31,415,926,535,897 base-10 digits of pi are now known.
Does it mean that if we have a list of, say, 10,000 digits of pi that starts with the 40,000,000,000,000th digit of pi, we won't recognize it as coming from pi (secretely computed so far by someone)? I guess we won't -- as pi digits look random.
What about a 10,000 digits list of zeros and ones starting with the 40,000,000,000,000th digit of the Kolakoski seq? (again, let's imagine someone has secretely computed that). Is there a test that could give us a hint (the difference with pi being that Kolakoski is a selfdescribing sequence)?
Thanks, É.
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