Template:Sequence of the Day for September 16

Intended for: September 16, 2011

Timetable

• First draft entered by Alonso del Arte on September 4, 2011 ✓
• Draft reviewed by Daniel Forgues on September 15, 2012 ✓
• Draft to be approved by August 16, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A059742: Decimal expansion of

π + e

.

5.859874482...

We don’t know whether

π + e

is irrational (let alone transcendental) or not. We know that both

e

and

π

are not only irrational, but also transcendental. Does it naturally follow that their sum is irrational (and if so, then transcendental)? Or would that be jumping to conclusions?

It is not known whether the following are irrational (let alone transcendental) or not:

• π + e and π  −  e
• π ⋅  e and π  / e
• π  e

It is known that the following is transcendental (thus irrational):

• e  π (Gelfond’s constant)