Nice to have another go at something.
I see that your last post came before I finished an edit to my previous post (#5), and so you might like to have a look at that one.
I wrote a small, clunky, BASIC program to get my results, and can't think of a cleverer approach.
It's interesting that all my results for the lowest n have n=131...which looks like a pattern to me.
But it all seems rather frivolous, and so I think I'll leave it there.
]]>Great to hear from you.
Just knocked together a short prog. to crunch this. Couldn't do better than 131.
Is there a way to get this analytically I wonder?
Bob
]]>Assuming it's the first three, I have found an 'n' that is lower than 1000. I got 0.167989....Bob
Hi Bob,
For 167dddd..., I got m=22, n=131, m/n=0.1679389...
Did you omit the '3' that's in my quotient, or did you find a different n than 131?
Here's the complete list of lowest n I found:
167dddddd... : m=22, n=131, m/n=0.167938931...
d167ddddd... : m=107, n=131, m/n=0.816793893...
dd167dddd... : m=50, n=131, m/n=0.381679389...
ddd167ddd... : m=5, n=131, m/n=0.038167938...
dddd167dd... : m=66, n=131, m/n=0.503816793...
ddddd167d... : m=59, n=131, m/n=0.450381679...
dddddd167... : m=19, n=131, m/n=0.145038167...
And for all such {167dddddd,d167ddddd,...dddddd167}, I found that the next-to-lowest n is 137.
]]>I am not yet claiming that is the lowest 'n'. Still working on it.
B
]]>Remember this isn't my problem.
It says '3 digits are'; it's unclear if that means the first three or any three. It doesn't say the decimal is just 0.167 There may be more digits after that.
Assuming it's the first three, I have found an 'n' that is lower than 1000. I got 0.167989....
If the answer may be 0.dddd167dddd then I think I could get an even lower n.
Bob
]]>