You should make a YouTube channel with aolitions to all these puzzles. I would watch it
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We already have one =)https://www.youtube.com/channel/UCSD2RxaYn2Nxkm41gp-eKfA …
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Generating function of Fibonacci sequence is power series. In this case denominator is of 100ⁿ-10ⁿ-1 form which creates these interesting patterns:pic.twitter.com/Eu7ZNHs0Ew
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Greatly
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I am always interested by your tweets even though I don’t have a clue as to what you are talking about.
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because each natural number can be interpreted only as the sum of one or more different fibonacci numbers in such a way that the sum does not include two consecutive fibonacci numbers
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Because I can plug any base of my choosing in the generating function of the fibonacci sequence: f(z)=1/(1-z(1+z)). In this case, plugging in z=1/10^k does the trick.
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Yes, but math with sub/super-scripts in a tweet get messy. Set up infinite sum, use recurrence relation of F_n, and solve.
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wow!!!!!
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Sum the series of terms F_k/10^k using the recursive relation for the Fibonacci numbers. You can do the same for F_k/(10^d)^k for any d
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