20131129, 15:40  #1 
Feb 2012
Prague, Czech Republ
A9_{16} Posts 
[Curiosity] Binary logarithm of a Mersenne number
The binary logarithm[0] of a Mersenne number , having enough precision to
reconstruct exactly after rounding to an integer, ie. < is .  The integral part of is . The fractional part of consists of binary ones. For example: Code:
n L L (base 2)  1 0 0 2 1.5 1.1 3 2.75 10.11 4 3.875 11.111 5 4.9375 100.1111 ... 
20131129, 22:15  #2 
∂^{2}ω=0
Sep 2002
República de California
2^{6}·181 Posts 
So 3 = 2*sqrt(2), then? Interesting  had not realized that. Learn something new every day around here.

20131130, 03:39  #3 
Feb 2012
Prague, Czech Republ
13^{2} Posts 

20131130, 05:35  #4 
Romulan Interpreter
Jun 2011
Thailand
3^{4}·113 Posts 
Puzzle: Does the error (why would you need the absolute of it? Mn is always bigger) converges? And if so, to what?
(Hint: ) (grrr, why \dif doesn't work here? also, I can't hide stuff?) Last fiddled with by LaurV on 20131130 at 06:12 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Binary pattern in p for Mersenne prime 2p1  TrdH  Miscellaneous Math  41  20140317 00:35 
Mersenne Digits Curiosity  davar55  Lounge  11  20130208 15:19 
calculate logarithm base 2 of number very close 1  thehealer  Other Mathematical Topics  9  20110420 14:02 
Discrete logarithm mod Mersenne primes?  Unregistered  Information & Answers  0  20060827 15:32 
Binary representation prime number of 1's.  TTn  15k Search  0  20041218 21:10 