I think there's more than this, if I get what David was hinting at. Rot13, so as not to give it away: Qnivq'f ahzore snpgbef nf n cebqhpg bs gjb fznyyre ahzoref, juvpu fgvyy funer n pbzzba snpgbe. Zberbire, nyy bs vgf cevzr snpgbef ner Zrefraar cevzrf! Truly remarkable, David!
The 27, 37 example is the smallest pair that isn't just a trivial repeat of 1/9=.1111... or 1/3 = .3333...
But yes, you're right. I didn't want to give away too much of the answer of David Wilson's exercise to the reader. . . but, spoilers and many examples at [1]
- Robert
[1] http://mrob.com/pub/math/numbers-12.html#lb999
On Sun, Feb 5, 2012 at 00:44, Tom Duff <td@pixar.com> wrote:
Robert Munafo <mrob27@gmail.com> writes:
Hey that's cool, and they're much like my favorite such pair, 1/27=0.037037037... and 1/37=0.027027027... I'll add them to my numbers pages!
I suspect these are pretty thick on the ground. For example we have 1/303 = 0.0033 0033 0033 ... and 1/33 = 0.0303 0303 0303 ...
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com