Template:Sequence of the Day for April 30

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

113 x   ≈   14.60157

and

127 x   ≈   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.