A non-integer that's the same in binary and ternary after the Nth digit

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Keith F. Lynch

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Jun 22, 2022, 12:19:49 AM6/22/22
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I found a non-integer that has the same expansion in binary and in
ternary after the Nth digit. I'll post it in a week if nobody beats
me to it.

In other words, something that looks like:

binary: 0.0110100110010110100111...
ternary: 0.1221100110010110100111...

(Not an actual example.)
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Keith F. Lynch - http://keithlynch.net/
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Keith F. Lynch

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Jun 22, 2022, 12:20:57 AM6/22/22
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Keith F. Lynch

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Sep 9, 2022, 11:07:21 PM9/9/22
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Hen Hanna <henh...@gmail.com> wrote:
> Keith F. Lynch wrote:
>> I found a non-integer that has the same expansion in binary and in
>> ternary after the Nth digit. I'll post it in a week if nobody beats
>> me to it.

> if you dont want to post "it" mabye you could post an easier
> problem... Thanks !

Sorry I didn't get around to posting earlier.

1/24, 3/20, 7/20, and 11/24. Also 1/2 with a non-standard
representation. Also each of these added to any integer.

Hen Hanna

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Sep 10, 2022, 1:40:30 AM9/10/22
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0.0111111111... (in Binary) == 0.49999999... is obvious, but i wasn't familiar with:

0.1111111111... (in Base 3) == 0.49999999... == 1/2


i wish Martin Gardner were alive, so i could tell him about this !
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