A366421 a(n) is the floor of the n-th improper fraction (including the ones of the type n/n) sorted by increasing numerator+denominator, then by numerator.

1, 2, 1, 3, 1, 4, 1, 2, 5, 1, 2, 6, 1, 1, 3, 7, 1, 2, 3, 8, 1, 1, 2, 4, 9, 1, 1, 2, 4, 10, 1, 1, 2, 3, 5, 11, 1, 1, 2, 3, 5, 12, 1, 1, 1, 2, 3, 6, 13, 1, 1, 2, 2, 4, 6, 14, 1, 1, 1, 2, 3, 4, 7, 15, 1, 1, 1, 2, 3, 4, 7, 16, 1, 1, 1, 2, 2, 3, 5, 8, 17, 1, 1, 1, 2, 2, 3, 5, 8, 18

Offset

1,2

Links

Table of n, a(n) for n=1..90.

Formula

a(n) = floor[A138099(n)/(A216607(n)+1)]

Example

The first such fraction is 1/1, followed by 2/1, 2/2, 3/1, 3/2 and so on, then a(1)=[1/1]=1, a(2)=[2/1]=2, a(3)=[2/2]=1, a(4)=[3/1]=3, a(5)=[3/2]=1 and so on, where [.] is the floor function.
Terms begin:
  [1/1]=1,
  [2/1]=2,
  [2/2]=1, [3/1]=3,
  [3/2]=1, [4/1]=4,
  [3/3]=1, [4/2]=2, [5/1]=5,
  [4/3]=1, [5/2]=2, [6/1]=6,
  ...

Crossrefs

Sequence in context: A210256 A332422 A229944 * A218533 A328578 A351613

Adjacent sequences: A366418 A366419 A366420 * A366422 A366423 A366424

Keyword

nonn

Author

Mariano Masiello, Nov 16 2023

Status

approved