A079938 Greedy frac multiples of Pi: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi.

1, 2, 3, 8, 99, 33102, 66317, 265381, 1360120

Offset

1,2

Comments

The n-th greedy frac multiple of x is the smallest integer that does not cause Sum_{k=1..n} frac(a(k)*x) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x.

Links

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

Example

a(4) = 8 since frac(1x*) + frac(2*x) + frac(3*x) + frac(8*x) < 1, while frac(1*x) + frac(2*x) + frac(3*x) + frac(k*x) > 1 for all k > 3 and k < 8.

Maple

Digits := 100: a := []: s := 0: x := Pi: for n from 1 to 10000000 do: temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a), n]: print(n): s := s+evalf(frac(n*x)): fi: od: a;

Crossrefs

Cf. A002486 (denominators of convergents to Pi), A079934, A079937, A079939.

Sequence in context: A368246 A243954 A005008 * A324006 A112237 A371225

Adjacent sequences: A079935 A079936 A079937 * A079939 A079940 A079941

Keyword

more,nonn

Author

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

Extensions

One more term from Mark Hudson, Jan 30 2003

Status

approved