OFFSET
1,3
COMMENTS
a(n) is nondecreasing; lim_{n->oo} a(n) = oo.
Swapping the x and y coordinate of the sequence does not yield the sequence defined as the point where x + y = n, x and y are integers and x/y is as close as possible to 1/Pi even when excluding terms that would lead to a division by 0.
FORMULA
a(n) is either ceiling(n*Pi/(1+Pi)) or floor(n*Pi/(1+Pi)).
a(n) = round((2*n*Pi + n - sqrt(Pi^2 + 2*Pi + n^2 + 1))/(2*Pi + 2)). - Jon E. Schoenfield, Nov 17 2023
EXAMPLE
For n = 3, the possible fractions are (0,3), (1,2), (2,1) as any negative values would would be further from Pi than 0/3. The closest fraction to Pi out of these is 2/1 so a(3) = 2.
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Colin Linzer, Nov 09 2023
EXTENSIONS
Corrected information and made it in line with A367194.
STATUS
approved