Template:Sequence of the Day for April 18

Intended for: April 18, 2013

Timetable

• First draft entered by Alonso del Arte on April 6, 2012 ✓
• Draft reviewed by Daniel Forgues on April 18, 2016 ✓
• Draft to be approved by March 18, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A173898: Decimal expansion of sum of the reciprocals of the Mersenne primes.

0.51645417894078856533048734297...

Even though we don’t know whether there are any more Mersenne primes than the forty-odd we know, we do know that this number is less than the sum of reciprocals of all the Mersenne numbers* (A001348), which itself is less than the sum of reciprocals of numbers of the form

2 n  −  1

(the Erdős–Borwein constant, see A065442). However, unlike that other number, we don’t know if it’s irrational: disproving that would require a proof of the finiteness of the set of Mersenne primes.

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* Mersenne numbers usually refer to numbers of the form

2 p  −  1

, where

p

is prime (

2 p  −  1

is either prime or composite).