A233208 A measure of quality (the higher the better) for the approximation to e by rationals A022852(n)/n.

3, 2, 6, 7, 2, 3, 35, 3, 2, 5, 10, 2, 2, 17, 4, 2, 4, 14, 2, 2, 11, 5, 2, 4, 23, 3, 2, 8, 5, 2, 3, 66, 3, 2, 7, 7, 2, 3, 76, 3, 2, 5, 8, 2, 3, 24, 4, 2, 5, 11, 2, 2, 14, 4, 2, 4, 17, 2, 2, 10, 5, 2, 3, 33, 3, 2, 8, 6, 2, 3, 502, 3, 2, 6, 7, 2, 3, 38, 3, 2, 5, 9, 2, 2, 18, 4, 2, 4, 13, 2, 2, 12, 5, 2, 4, 22

Offset

1,1

Comments

a(n) is the greatest natural number such that abs( n*e-A022852(n) ) < 1/a(n). Trivially a(n)>=2. a(n)=2 iff n is in A191104 (easy proof).

Links

Table of n, a(n) for n=1..96.

Formula

a(n) = floor( 1 / abs( n*e-A022852(n) ) ).

Example

a(7) = 35 because floor(1/abs(7*e-19)) = floor(1/0.0279727...) = floor(35.749...) = 35.

Prog

(PARI) a(n)=floor(1/abs(n*exp(1)-round(n*exp(1)))) \\ Ralf Stephan, Dec 13 2013

Crossrefs

Cf. A022852. For records see A233209, A007677.

Sequence in context: A087237 A275630 A102004 * A196518 A207636 A125764

Adjacent sequences: A233205 A233206 A233207 * A233209 A233210 A233211

Keyword

nonn

Author

Franz Vrabec, Dec 06 2013

Extensions

More terms from Ralf Stephan, Dec 13 2013

Status

approved