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Template:Sequence of the Day for September 24

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Intended for: September 24, 2012

Timetable

  • First draft entered by Daniel Forgues on September 23, 2012
  • Draft to be reviewed by July 24, 2012
  • Draft to be approved by August 24, 2012
Yesterday's SOTD * Tomorrow's SOTD

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A077761: Decimal expansion of Mertens’ constant (also known as the Hadamard–de la Vallée-Poussin constant), or prime reciprocal constant.*

B1  = 
π (n)
i   = 1
  
1
pi
 
− log  log n
,
where
π (n)
is the prime counting function and
pi
is the
i
-th prime number.
0.2614972128476427837554...

Today’s SOTD is about the harmonic series of the primes (sum of the reciprocals of the primes), September 26’s SOTD will be about the sum of alternating series of reciprocals of primes.

_______________
* Weisstein, Eric W., Mertens Constant, from MathWorld—A Wolfram Web Resource.