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A079938 Greedy frac multiples of Pi: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi. 4
1, 2, 3, 8, 99, 33102, 66317, 265381, 1360120 (list; graph; refs; listen; history; text; internal format)
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: A319218 A243954 A005008 * A324006 A112237 A132502

Adjacent sequences:  A079935 A079936 A079937 * A079939 A079940 A079941

KEYWORD

more,nonn,changed

AUTHOR

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

EXTENSIONS

One more term from Mark Hudson, Jan 30 2003

STATUS

approved

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Last modified April 23 05:42 EDT 2021. Contains 343199 sequences. (Running on oeis4.)