A367193 The x-coordinate of the point where x + y = n, x and y are integers and x/y is as close as possible to Pi.

0, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 48, 49, 49, 50, 51, 52

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.

Links

Table of n, a(n) for n=1..68.

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

Cf. A367194 (y-coordinate), A000796, A002485.

Sequence in context: A195180 A069210 A195172 * A277425 A245335 A244230

Adjacent sequences: A367190 A367191 A367192 * A367194 A367195 A367196

Keyword

nonn,frac

Author

Colin Linzer, Nov 09 2023

Extensions

Corrected information and made it in line with A367194.

Status

approved