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

1,6

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..74.

Formula

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

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) = 1.

Maple

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

Crossrefs

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

Sequence in context: A108955 A108956 A289133 * A135297 A176146 A171481

Adjacent sequences: A367191 A367192 A367193 * A367195 A367196 A367197

Keyword

nonn,frac

Author

Colin Linzer, Nov 13 2023

Status

approved