in reply to Re^3: Can It Be Written In Base X With Only 1s And 0s
in thread Can It Be Written In Base X With Only 1s And 0s

All of them can be defined as the sums of multiples of powers of 3.

All integers are sums of multiples of powers of 3. The ones of interest are sums of powers of 3. You had it right the first time

  • Comment on Re^4: Can It Be Written In Base X With Only 1s And 0s

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Re^5: Can It Be Written In Base X With Only 1s And 0s
by BrowserUk (Patriarch) on Jun 16, 2015 at 13:04 UTC

    Jeez!

    These are all powers of 3 less than 3^11:

    1 3 9 27 81 243 729 2187 6561 19683 59049

    [download]

    These are all sums of multiple powers of three less than 3^11 that also consist of 0s & 1s when encoded in base-3:

    <Reveal this spoiler or all in this thread>

    It is a quicker to permute the combinations of the 11 powers of the to look for solutions that are sum of distinct powers of 3,

    than it is to permute the combinations 1847 compliant numbers that are (a subset of the) sums of multiple powers of 3.

    And the numbers & differences get much larger for 4, 5, 6 ...

    So, please refrain from telling me what I got right and wrong, when you appear to not understand the subject.

    With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority". I'm with torvalds on this
    In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked
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      So, please refrain from telling me what I got right and wrong,

      If it wasn't wrong, why did you change what I said was wrong? You changed "sums of multiples of powers of 3" (wrong, since 6 is such a number) to "sums of multiple powers of three" (right, since 6 isn't such a number).

      As for "not understanding", I posted a solution that finds the permutations long before your first post to the thread.

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        I think you must be confusing this with something from another site; or your just misremembering what you thought you read and have't checked back to see your error.

        1. I didn't change anything. (Please ask tye to verify that I made no edits at all!)

          The only post in the entire thread that contains the phrase "sums of multiple powers of three"; is yours. (Or was Until I posted this response.)

        2. And I didn't mention 6 anywhere.

        And with your parentheticals, it makes even less sense; since "6" isn't mention in either of your (mis) quotes; nor in the post to which you responded.

        Quite where you dreamed that your saw something that needed your correction; I can only hazard a guess. (Good stuff was it?)

        Why you then comeback and defend it with a bunch of made up crap; is just vintage ikegami.

        With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority". I'm with torvalds on this
        In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked
[reply]

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