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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, 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.
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
KEYWORD
nonn,frac
AUTHOR
Colin Linzer, Nov 13 2023
STATUS
approved