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Template:Sequence of the Day for September 22

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Intended for: September 22, 2012

Timetable

  • First draft entered by Frank Ellerman on September 22, 2011
  • Draft reviewed by Charles Greathouse on September 23, 2011
  • Draft approved by Alonso del Arte on April 1, 2012
Yesterday's SOTD * Tomorrow's SOTD

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A079614: Bertrand’s constant.

1.251647597790463...
Bertrand’s postulate shows that for each
n > 3
there is at least one prime
n < p < 2 n  −  2
. Likewise for
n > 1
there is at least one prime
n < p < 2 n
. Therefore a constant
b
exists where
⌊  2b
,
⌊  2 2b
, ,
⌊  2 2 2b
,
are all primes (cf. A051501). Finding more digits for
b
requires finding better bounds for the prime counting function.