Template:Sequence of the Day for September 26

Intended for: September 26, 2012

Timetable

• First draft entered by Alonso del Arte on April 7, 2012 ✓
• Draft reviewed by Daniel Forgues on September 24, 2012 ✓
• Draft to be approved by August 26, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A078437: Decimal expansion of sum of alternating series of reciprocals of primes

∑ ∞ i   = 1 ( − 1) i  − 1 1 pi  .

0.26960635197167...

Here is another reminder of the infinitude of prime numbers. We may think we know a lot of prime numbers, but when it comes to computing this alternating series, this is the most precise we can get. The next digit is 4 or 5, we can’t say for sure just yet.

Today’s SOTD is about the sum of alternating series of reciprocals of primes, September 24’s SOTD was about the harmonic series of the primes (sum of the reciprocals of the primes).