A079941 Greedy frac multiples of log(2): a(1)=1, Sum_{n>0} frac(a(n)*log(2)) = 1.

1, 3, 6, 13, 26, 39, 277, 642, 2291, 4582, 6231, 16402, 26573, 36744, 63317, 73488, 110232, 414355, 828710, 1206321, 2412642, 4410929, 5617250, 12026466, 31668469, 51310472, 70952475, 141904950, 394046381

Offset: 1

Author

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

Keywords

• nonn
• more
• changed

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.

Examples

			a(4) = 13 since frac(1x) + frac(3x) + frac(6x) + frac(13x) < 1, while frac(1x) + frac(3x) + frac(6x) + frac(k*x) > 1 for all k>6 and k<13.
		

Crossrefs

Cf. A079943 (denominators of convergents to ln2), A079934, A079939, A079940.

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003

a(20)-a(29) from Sean A. Irvine, Aug 31 2025