127*Sqrt(62)

XYYXF · 2007-11-07, 22:53

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!

R. Gerbicz · 2007-11-07, 23:40

http://www.research.att.com/~njas/sequences/A098597

m_f_h · 2007-12-08, 12:31

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)

2007-11-07, 22:53	#1
XYYXF Jan 2005 Minsk, Belarus 400₁₀ Posts	*127Sqrt(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!

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
NFS sqrt by hand	henryzz	Factoring	18	2010-09-26 00:55
msieve C157 sqrt error: relation xxxx corrupt	tgrdy	Msieve	6	2010-08-20 21:51
ggnfs sqrt problem	hallstei	Factoring	7	2007-05-01 12:51
SQRT Problem	R.D. Silverman	NFSNET Discussion	11	2006-07-20 17:04
P(n+1)<(sqrt(P(n))+1)^2	Crook	Math	3	2005-10-26 21:29

2007-11-07, 23:40	#2
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 2⁵·7² Posts	http://www.research.att.com/~njas/sequences/A098597