Comments on: The Pinocchio and Oihcconip Sequences
https://blog.tanyakhovanova.com/2022/05/the-pinocchio-and-oihcconip-sequences/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Mon, 16 May 2022 23:00:53 +0000
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By: Pinocchio. No: Oihcconip. No, both. – The nth Root
https://blog.tanyakhovanova.com/2022/05/the-pinocchio-and-oihcconip-sequences/#comment-13448
Mon, 16 May 2022 23:00:53 +0000https://blog.tanyakhovanova.com/?p=1629#comment-13448[…] Essentially, “exploding dots” is a machine made of a row of boxes with rules describing how the dots loaded into the machine explode. As an example, let me describe the 1←2 machine, which corresponds to base 2. We load N dots into the rightmost box. Whenever there are 2 dots in one box, they explode into 1 dot in the box to the left. … (Tanya Khovanova) […]
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By: Andrew
https://blog.tanyakhovanova.com/2022/05/the-pinocchio-and-oihcconip-sequences/#comment-13446
Sun, 15 May 2022 06:14:17 +0000https://blog.tanyakhovanova.com/?p=1629#comment-13446It’s interesting how base 3/2 behaves in terms of prefixes. Adding a 0 to the end of a number does, in fact, multiply it by 3/2, justifying the name… but consider “21” = 4; “210” = 6; “2100” = 9; “21000”… well, you can’t multiply 9 by 3/2 and get an integer, so it follows that “21000” isn’t an integer, and neither are “21001” or “21002”, since they differ from “21000” by an integer. “21010” is okay since it differs from “21000” by “10”, also a half-integer. However, you’ll never find any integer that has “2100” as a proper prefix… since “21000” is a half-integer, “210000” is a quarter-integer, and can’t be rescued from that fate by the addition of any two-digit number.
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