Template:Sequence of the Day for January 1

Intended for: January 1, 2012

Timetable

• First draft entered by Alonso del Arte on October 30, 2011 based on remarks by Tilman Piesk ✓
• Draft preliminary review by Daniel Forgues on November 6, 2011 ✓ (to be completed)
• Draft to be approved by December 1, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A194602: Partitions interpreted as binary numbers.

{ 0, 1, 3, 5, 7, 11, 15, 21, ... }

The compositions of

n

correspond to

2 n   − 1

binary numbers. As partitions of

n

can be seen as compositions with addends ordered by size, binary numbers can also be assigned to partitions. The finite sequence of such binary numbers for partitions of

n

(in lexicographical order) is the beginning of the sequence for partitions of

n + 1

, which leads to an infinite sequence.