A079943 -id:A079943 - cp's OEIS frontend

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

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

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.

			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.

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

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

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

A079942 Numerators of the convergents of the continued fraction for log(2).

Original entry on oeis.org

0, 1, 2, 7, 9, 61, 192, 253, 445, 1143, 1588, 2731, 4319, 7050, 25469, 261740, 287209, 548949, 836158, 2221265, 3057423, 5278688, 8336111, 13614799, 49180508, 111975815, 385107953, 497083768, 6847196937, 48427462327, 200557046245, 248984508572, 449541554817

Offset: 1

Paul D. Hanna, Jan 19 2003

			9/13 = 0.6923076923076923...
61/88 = 0.69318181818181818...
192/277 = 0.6931407942238267148...
...
log(2) = 0.6931471805599453...

Cf. A002162 (decimal expansion of log(2)), A079941, A079943 (denominators).

Convergents[ContinuedFraction[Log[2],40]]//Numerator (* Harvey P. Dale, Jun 05 2021 *)

Corrected and extended by Harvey P. Dale, Jun 05 2021

cp's OEIS Frontend

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

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