# Some unpublished notes of Hofstadter

I'm looking for some unpublished notes called "Eta Lore," which are apparently related to a talk Douglas Hofstadter first gave at the Stanford Math Club in 1963. I know these notes exist because they're cited in the following articles:

I've e-mailed the authors of the articles above, but I also thought I'd try asking around here, since none of the authors who've responded so far have been able to help. Any information on alternative references would also be appreciated.

Motivation and Background

I'm specifically interested in the definition of the function INT mentioned in Section I.33 of Gödel, Escher, Bach. The description there, in case it rings any bells, is: "The basic idea behind INT is that plus and minus signs are interchanged in a certain kind of continued fraction."

As far as I can tell, the notes I'm looking for are mostly about continued fractions and integer sequences---in particular, things called $\eta$-sequences and $\beta$-sequences (unfortunately, I have no idea what those are, and I haven't found any leads on OEIS).

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Have you contacted Hofstadter? He is alive and working: cogs.indiana.edu/people/homepages/hofstadter.html – David Speyer Jul 3 '11 at 1:14
The link should be updated to cogs.indiana.edu/people/profile.php?u=dughof – Andrés Caicedo Dec 15 '13 at 7:10
@DavidSpeyer, thanks for the suggestion! It should have been obvious, but wasn't to me at the time. I did get in touch with Hofstadter, and he send me a copy of the notes. (I'm sorry this thank-you was so long in coming, by the way---I completely forgot I'd asked this question, and was only reminded when it popped up on the front page again.) – Vectornaut Dec 15 '13 at 7:28
@Vectornaut Can you send me his notes too? – Alexey Ustinov Dec 15 '13 at 12:53
@Vectornaut (or Alexey) Could either of you forward it to me as well? – Greg Zitelli Dec 15 '13 at 17:20

This graph is looks like a graf of the function which replaces partial quotient (in nearest integer continued fraction) in the following way: $$a_i+~\leftrightarrow~a_i+1-.$$ For example $$0+\cfrac{1}{3-\cfrac{1}{4+\cfrac{1}{5+0}}}\leftrightarrow 1-\cfrac{1}{2+\cfrac{1}{5-\cfrac{1}{6-0}}}.$$ \begin{align*} \frac{1}{2}=\frac{1}{2+0}&\leftrightarrow1-\frac{1}{3-0}=\frac{2}{3},&\frac{1}{3}=\frac{1}{3+0}&\leftrightarrow1-\frac{1}{4-0}=\frac{3}{4},\\ \frac{2}{5}=\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow1-\frac{1}{3-\frac{1}{3-0}}=\frac{5}{8},&\frac{3}{5}=1-\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow 0+\frac{1}{3-\frac{1}{3-0}}=\frac{3}{8}. \end{align*} The picture from the book: