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

Author

Colin Linzer, Nov 09 2023

Keywords

• nonn
• frac

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.

Examples

			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.

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

Extensions

Corrected information and made it in line with A367194.