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From: bob@burdvax.UUCP
Newsgroups: net.math
Subject: Re: binary expansion of 1/n
Message-ID: <1328@burdvax.UUCP>
Date: Mon, 28-Nov-83 15:47:11 EST
Article-I.D.: burdvax.1328
Posted: Mon Nov 28 15:47:11 1983
Date-Received: Wed, 30-Nov-83 02:14:10 EST
References: <685@sunybcs.UUCP>
Organization: SDC - a Burroughs Company, Paoli PA
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The least positive integer n for which the non-trivial binary
expansion of 1/n contains more 1's than 0's is 187.
The binary expansion of 1/187 has a 40-bit period containing 21 1's
and 19 0's.

The table below shows all values of n < 1000 which share this property.
This was achieved by brute force investigation (with grateful
acknowledgement to the Vax 11/780).  Does anyone have a generating function
for such numbers?


  n  period 1's  0's
 --- ------ ---  ---
 187   40   19   21
 323   72   35   37
 374   40   19   21
 427   60   28   32
 549   60   29   31
 559   84   41   43
 646   72   35   37
 687   76   37   39
 721   51   25   26
 748   40   19   21
 779  180   85   95
 781   70   32   38
 854   60   28   32
 927  102   50   52
 937  117   58   59
 965   96   47   49
 973  138   65   73