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Template:Sequence of the Day for October 14

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Intended for: October 14, 2011

Timetable

  • First draft entered by Alonso del Arte on August 8, 2011
  • Draft reviewed by Mitch Harris on August 9, 2011
  • Draft to be approved by September 14, 2011
Yesterday's SOTD * Tomorrow's SOTD

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A008619:
1 +
⌊  n / 2⌋
, n   ≥   0.
(Positive integers repeated twice.)
{ 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, ... }
Smallest positive integer whose harmonic mean with another positive integer is
n
. For example,
a (6) = 4
is already given (as 4 is the smallest positive integer such that the harmonic mean of 4 (with 12) is 6) —but the harmonic mean of 2 (with  −  6) is also 6 and 2 < 4, so the two positive integer restrictions need to be imposed to rule out both 2 and  −  6.

Note also that this sequence is the second outermost diagonal of Lozanić’s triangle.