The sequence in question is https://oeis.org/A027878. Please also add any useful comments to that entry! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Wed, Jul 13, 2016 at 11:45 AM, James Propp <jamespropp@gmail.com> wrote:
Yes, absolutely. That's why the initial and final digits behave so nicely. I should've mentioned that.
Jim
On Wednesday, July 13, 2016, Joerg Arndt <arndt@jjj.de> wrote:
Note that product(n>=1, 1-10^{-n}) is essentially Dedekind's eta function and Euler's pentagonal number theorem (to name just one) may be helpful with spotting patterns in the expansion.
Best regards, jj
* James Propp <jamespropp@gmail.com <javascript:;>> [Jul 13. 2016 08:00]:
One side-alley that I glanced down when I was preparing my current Mathematical Enchantments essay, but then resolutely marched myself past, involves the behavior of the decimal expansion of the product (10^1-1)(10^2-1)...(10^n-1); the initial and final digits are quite orderly, while the digits in the middle look random. Has anyone looked into this? It'd be especially interesting if one could establish some sort of phase transition.
I realize I'm using vocabulary loosely; there's no randomness involved, so we're not really doing stat mech. Still, some of the concepts of stat mech might apply.
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