Template:Sequence of the Day for January 2

Intended for: January 2, 2012

Timetable

• First draft entered by Alonso del Arte on October 30, 2011 ✓
• Draft reviewed by Daniel Forgues on November 6, 2011 ✓
• Draft to be approved by December 2, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A004676: Primes written in base 2.

{ 10, 11, 101, 111, 1011, 1101, 10001, ... }

Since 2 is the only even prime, then of course it is the only one that ends in zero in base 2. This highlights the oddity of 2 being the only even prime number.

The Fermat primes (only five are known!) are the only primes with binary weight equal to two: {11, 101, 10001, 10000001, 10000000000001, ...more???}

The repunits (base 2) are the Mersenne primes.