W2 and Kakeya constants

[N. J. A. Sloane]

Steve Finch posted this to the mathfun list:

Two constants listed at Simon Plouffe's website

   http://www.lacim.uqam.ca/piDATA/w2.txt
and
   http://www.lacim.uqam.ca/piDATA/kakeya.txt

have defied all my scholarly attempts to find
references:

   W2 constant = 1.52995403705719287491319417231
and
   K constant = 15.3377230231024356717285601672

Note: the Kakeya constant listed here seems to 
unrelated to the "Kakeya-Besicovitch constant"
that appears in geometry:

   http://pauillac.inria.fr/algo/bsolve/constant/kb/kb.html

Eric Weisstein, in his online encyclopedia, indicated
that K might be related to Khintchine's constant. 

These remain great mysteries to me. If anyone 
recognizes these and knows where in the literature
I should be looking, please e-mail me.  Thank you!

                                Steve Finch


Steven Finch                            
MathSoft Engineering & Education, Inc.                   
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