At 10:36 PM 12/3/02 -0500, you wrote:
I saw your name listed by information about the number of ones in the binary expansion of 3^n. Do you know any way of getting an analytic formula or references to any material relating to a formula for this?
Gershon Bialer I assume you are talking about my credit on Sloane's Encyclopedia of Integer Sequences, sequence A011754. I had written a program to display the powers of 3 as a bit-raster (a rather interesting display, it turns out) and it was cheap to count the ones. So I did, and it turned out that Sloane didn't have that one, so I got credit.
If you actually look at the bit-map (this is probably a three-line program in Mathematica, or you can look at the picture in the given reference at EIS), you will see why I think there will be no easy formula for this sequence. I'd bet that the cheapest way to calculate the nth element of the sequence will always be to actually compute 3^n and just count. I have taken the liberty of cc-ing this answer to a list of recreational math enthusiasts, one of whom may have more insight. -A