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Template:Sequence of the Day for April 30

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Intended for: April 30, 2013

Timetable

  • First draft entered by Alonso del Arte on April 6, 2012
  • Draft reviewed by Daniel Forgues on April 26, 2012
  • Draft to be approved by March 30, 2013
Yesterday's SOTD * Tomorrow's SOTD

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A038458: Decimal expansion of Smarandache's constant.

0.567148130202...
Given two consecutive primes
p
and
q
, what is the smallest positive real number
x
such that
q  x  −  p  x = 1
? If
p = 113
and
q = 127
, then the answer is Smarandache's constant. (We verify that
113x   ≈   14.60157
and
127x   ≈   15.60157
.) Sukanto Bhattacharya conjectures that this number is irrational. Of course if
p = 2
and
q = 3
, the answer
x = 1
is not quite so interesting.