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-   -   127*Sqrt(62) (https://www.mersenneforum.org/showthread.php?t=9575)

XYYXF 2007-11-07 22:53

127*Sqrt(62)
 
Have you ever looked at its decimal expansion? :wink:

It appears to be

[TEX]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} - ...[/TEX]

where a = 1000.

Curious!

R. Gerbicz 2007-11-07 23:40

[URL="http://www.research.att.com/~njas/sequences/A098597"]http://www.research.att.com/~njas/sequences/A098597[/URL]

m_f_h 2007-12-08 12:31

[quote=R. Gerbicz;118002][URL="http://www.research.att.com/%7Enjas/sequences/A098597"]http://www.research.att.com/~njas/sequences/A098597[/URL][/quote]

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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