A367329 The y-coordinate of the point where x + y = n, x & y are integers and x/y is as close as possible to e.

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20

Offset

1,5

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/e even when excluding terms that would lead to a division by 0.

Links

Table of n, a(n) for n=1..74.

Example

For n = 3, the possible points are (0,3), (1,2), (2,1), as any negative fraction would would be further from e than 0/3. The closest fraction to e out of these is 2/1 so a(3) = 1.

Crossrefs

Cf. A001113 (e), A367328 (x-coordinate), A007677.

Sequence in context: A128929 A257839 A075245 * A328301 A129253 A008652

Adjacent sequences: A367326 A367327 A367328 * A367330 A367331 A367332

Keyword

easy,frac,nonn

Author

Colin Linzer, Nov 14 2023

Status

approved