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Template:Sequence of the Day for January 1

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Intended for: January 1, 2012


  • 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
correspond to
2n   − 1
binary numbers. As partitions of
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
(in lexicographical order) is the beginning of the sequence for partitions of
n + 1
, which leads to an infinite sequence.