A367193 -id:A367193 - cp's OEIS frontend

A367194 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.

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, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18

Offset: 1

Colin Linzer, Nov 13 2023

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.

			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.

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

f:= proc(n) local x;
   x:= floor(n/(1+Pi));
   if x = 0 then return 1 fi;
   if is((n-x)/x + (n-x-1)/(x+1) < 2*Pi) then x else x+1 fi
end proc:
map(f, [$1..100]); # Robert Israel, Nov 13 2023

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

cp's OEIS Frontend

A367194 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.

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