[math-fun] Integers with many 0s in base 2 and base 3 (fwd)

---------- Forwarded message ---------- Date: Sat, 21 Dec 2002 00:01:59 -0500 From: Andreas Weingartner <weingartner@suu.edu> To: NMBRTHRY@LISTSERV.NODAK.EDU Subject: Integers with many 0s in base 2 and base 3 Hello everybody: Here is a problem that comes up in quantum computation. I would appreciate any information on this problem. Prove or disprove: There exists an epsilon>0, such that no natural number has the property that in base 2 as well as in base 3, at most (epsilon)*100% of the digits are nonzero. Example: 513=(1000000001) in base 2 and 513=(201000) in base 3 so epsilon<1/3. Andreas