Template:Sequence of the Day for August 29

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

The line below marks the end of the <noinclude> ... </noinclude> section.

---

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.