A206788 Denominators of semiconvergents to log_2(3), which equals log(3)/log(2).

1, 1, 2, 3, 5, 7, 12, 17, 29, 41, 53, 94, 147, 200, 253, 306, 359, 665, 971, 1636, 2301, 2966, 3631, 4296, 4961, 5626, 6291, 6956, 7621, 8286, 8951, 9616, 10281, 10946, 11611, 12276, 12941, 13606, 14271, 14936, 15601, 16266, 31867, 47468, 79335, 111202, 190537

Offset

1,3

Comments

These are also equal divisions of the octave that have good approximations of the 3rd harmonic (and hence other Pythagorean intervals such as 3/2, 4/3, 9/8 etc.).

The semiconvergents are important musically as the cardinalities of MOS scales of Pythagorean tuning.

Links

Table of n, a(n) for n=1..47.

Wikipedia, Definition of continued fraction semiconvergents

Crossrefs

Cf. A028507 (continued fraction expansion), A005664 (denominators of convergents).

Sequence in context: A080528 A245152 A334271 * A002965 A206290 A091696

Adjacent sequences: A206785 A206786 A206787 * A206789 A206790 A206791

Keyword

nonn,frac,easy

Author

Keenan Pepper, Feb 12 2012

Status

approved