20131129, 15:40  #1 
Feb 2012
Prague, Czech Republ
10110001_{2} 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^{4}×727 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
3·59 Posts 

20131130, 05:35  #4 
Romulan Interpreter
Jun 2011
Thailand
2^{3}×1,193 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 
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