mersenneforum.org > Math 127*Sqrt(62)
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 2007-11-07, 22:53 #1 XYYXF     Jan 2005 Minsk, Belarus 6208 Posts 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!
 2007-11-07, 23:40 #2 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 2·33·29 Posts
2007-12-08, 12:31   #3
m_f_h

Feb 2007

24×33 Posts

Quote:
 Originally Posted by R. Gerbicz http://www.research.att.com/~njas/sequences/A098597
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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