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Template:Sequence of the Day for January 1

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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
2n   − 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.