Talk:Minimum positive multiple in base 10 using only 0 and 1: Difference between revisions
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:No idea, however I had four (unrelated) minor insights: 1) B10(n) where n is all-nines is all-ones, in fact 9*length(n) ones. 2) No smallest multiplier ends with 0. 3) B10(2n) is either B10(n) [If n ends in 5, I think] or B10(n)*10, and the multiplier must end in 5. 4) for B10(k*10+n) where n is odd {1,3,5,7,9}, the multiplier must end in {1,7,(2/4/6/8),3,9}. Note that between them, rules 3 and 4 cover a trailing {1..9}, once each. None of those really help explain anything though. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 15:36, 2 March 2020 (UTC) |
:No idea, however I had four (unrelated) minor insights: 1) B10(n) where n is all-nines is all-ones, in fact 9*length(n) ones. 2) No smallest multiplier ends with 0. 3) B10(2n) is either B10(n) [If n ends in 5, I think] or B10(n)*10, and the multiplier must end in 5. 4) for B10(k*10+n) where n is odd {1,3,5,7,9}, the multiplier must end in {1,7,(2/4/6/8),3,9}. Note that between them, rules 3 and 4 cover a trailing {1..9}, once each. None of those really help explain anything though. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 15:36, 2 March 2020 (UTC) |
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== general observations == |
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If the '''n''' is only composed of ones and zeros, then the '''B10''' is equal to '''n'''. |
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If the '''n''' is only composed of nines, then the '''B10''' is composed of the shown digits below: |
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::: For '''9''', the '''B10''' digits are '''12345678''', and change the last eight to a nine. |
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::: For '''99''', the '''B10''' digits are '''1122334455667788''', and change the last eight to a nine. |
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::: For '''999''', the '''B10''' digits are '''111222333444555666777888''', and change the last eight to a nine. |
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::: For '''9999''', the '''B10''' digits are '''11112222333344445555666677778888''', and change the last eight to a nine. |
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I'm sure there is a more elegant way of expressing this, but I think showing is better than telling (the pattern seems obvious enough). -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 22:48, 2 March 2020 (UTC) |