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Old 2007-11-07, 22:53   #1
XYYXF
 
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Jan 2005
Minsk, Belarus

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Default 127*Sqrt(62)

Have you ever looked at its decimal expansion?

It appears to be

a - a^{-1} - \frac12 a^{-3} - \frac12 a^{-5} - \frac58 a^{-7} - \frac78 a^{-9} - \frac{21}{16} a^{-11} - \frac{33}{16} a^{-13} - \frac{429}{128} a^{-15} - \frac{715}{128} a^{-17} - ...

where a = 1000.

Curious!
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Old 2007-11-07, 23:40   #2
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

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http://www.research.att.com/~njas/sequences/A098597
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Old 2007-12-08, 12:31   #3
m_f_h
 
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Feb 2007

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Quote:
Originally Posted by R. Gerbicz View Post
Well it is not so curious that sqrt(10^6-2) has that expansion
but (at least to me) the interesting part is the fact that 10^6-2=(2^8-1)^2*(2^5-1)*2
or 10^6/2-1 = 499999 = 127^2*31 (nice factorization into mersenne primes)
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