A079557 Numerator for global rational approximations.

2, 3, 5, 11, 31, 97, 469, 3767, 49729

Offset

1,1

Links

Table of n, a(n) for n=1..9.

Formula

a(n) is the smallest integer such that if 0< m1/a(m) < r1/a(r) < 1, m<n and r<n, then there is an integer n1 which satisfies m1/a(m) < n1/a(n) < r1/a(r), but there is no integer n2 with n2/a(n)=m1/a(m) or n2/a(n)=r1/a(r)

Example

a(3) is not 4 because 2/4 = 1/2, a(3)=5 because 0 < 1/5 < 1/3 < 2/5 < 1/2 < 3/5 < 2/3 < 4/5 < 1; a(4) is not 7 because if 1/3 < x/7 < 2/5 then x is not an integer

Crossrefs

Sequence in context: A087580 A072535 A073680 * A090709 A357220 A112279

Adjacent sequences: A079554 A079555 A079556 * A079558 A079559 A079560

Keyword

nonn

Author

F. A. González Lahoz, Jan 24 2003

Status

approved