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Template:Sequence of the Day for August 25

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Intended for: August 25, 2011

Timetable

  • First draft entered by Mitch Harris on August 3, 2011
  • Draft reviewed by Alonso del Arte on August 21, 2011
  • Draft approved by ??? on August 2?, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A002487: Stern’s diatomic series.

{ 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, ... }
Stern’s diatomic series is defined by the recursion
a (2n) = a (n), a (2n + 1) = a (n) + a (n + 1),
with base cases
a (0) = 0, a (1) = 1
.

It magically gives, by the ratio of any two successive entries, all positive rationals exactly once. It is essentially a breadth first traversal of the ratios of the nodes in the Stern–Brocot tree.