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Sequence of the Day

Sequence of the Day for October 14

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.

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Template:Today in Math History for October 14

Sequences in the news

Sequences in the News

  • Dec 25 2018 German Heise-News "integers, please" column explains A003173 and OEIS.
  • Feb 01 2018 Alphabet announced a $8,589,869,056 = $A000396(6) stock buyback.
  • Jan 03 2018 Largest known term of A000043 announced: 77232917.
  • Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
  • Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
  • Jan 19 2016 Largest known term of A000043 announced: 74207281, also discovered by Curtis Cooper.


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