A367194 - OEIS

%I #57 Jan 25 2024 07:14:56

%S 1,1,1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,

%T 8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,

%U 14,15,15,15,15,15,16,16,16,16,17,17,17,17,18,18

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

%C a(n) is nondecreasing; lim_{n->oo} a(n) = oo.

%C 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.

%F a(n) is always either ceiling(n/(1+Pi)) or floor(n/(1+Pi)).

%e 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) = 1.

%p f:= proc(n) local x;

%p    x:= floor(n/(1+Pi));

%p    if x = 0 then return 1 fi;

%p    if is((n-x)/x + (n-x-1)/(x+1) < 2*Pi) then x else x+1 fi

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Nov 13 2023

%Y Cf. A367193 (x-coordinate), A000796, A002486.

%K nonn,frac

%O 1,6

%A _Colin Linzer_, Nov 13 2023