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Template:Sequence of the Day for October 19

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Intended for: October 19, 2012

Timetable

  • First draft entered by Alonso del Arte on April 8, 2012
  • Draft reviewed by Daniel Forgues on October 18, 2012October 10, 2018
  • Draft to be approved by September 19, 2012
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A065918: Logarithm of
2 +
2  3
.
1.3169578969248...
This number figures in the search for Mersenne primes thus: the Mersenne number
M = 2n  −  1
is prime if and only if
M
divides

     
cosh (2n  − 2 log (2 +
2  3
 ))
 = 
e  + { 2n  − 2 log (2 +
2  3
 ) }
+ e  − { 2n  − 2 log (2 +
2  3
 ) }
2
 = 
(2 +
2  3
 )  + { 2n  − 2  } + (2 +
2  3
 )  − { 2n  − 2  }
2
 ,

where
cosh (x)
is the hyperbolic cosine function. David Wilson has proposed calling the number
log (2 +
2  3
 )
the Helms constant.
The number
2 +
2  3
= tan
5 π
12
= cot
π
12
is sometimes called the Kasner constant (see A019973 for decimal expansion).