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Template:Sequence of the Day for August 29

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Intended for: August 29, 2011

Timetable

  • First draft entered by Alonso del Arte on May 27, 2011 (as a verbatim copy of a write-up from December 27, 2010) ✓
  • Draft reviewed by Alonso del Arte on August 26, 2011
  • Draft approved by Daniel Forgues on August 28, 2012
Yesterday's SOTD * Tomorrow's SOTD

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A113307: Trott’s third constant: decimal expansion coincides with its non-simple continued fraction read serially.

0.48267728...

We verify that

     
0.4826772...  =  0 + 
4
8 + 
2
6 + 
7
7 + 
2
 .

M. Trott has discovered two other such constants.* (How many such constants are there for base 10?)

Since the concept is base-dependent, one might wonder what similarly defined constants are for, e.g., base 2 (binary) or base
ϕ
(phinary)!

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