A028507 Continued fraction expansion for log_2(3).

1, 1, 1, 2, 2, 3, 1, 5, 2, 23, 2, 2, 1, 1, 55, 1, 4, 3, 1, 1, 15, 1, 9, 2, 5, 7, 1, 1, 4, 8, 1, 11, 1, 20, 2, 1, 10, 1, 4, 1, 1, 1, 1, 1, 37, 4, 55, 1, 1, 49, 1, 1, 1, 4, 1, 3, 2, 3, 3, 1, 5, 16, 2, 3, 1, 1, 1, 1, 1, 5, 2, 1, 2, 8, 7, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 1, 5, 4, 2, 2, 2, 16, 8, 10, 1, 25, 2, 1

Offset

0,4

Links

T. D. Noe, Table of n, a(n) for n = 0..9999

Rafael Cubarsi, Extended Expressive Intonation: An Application of the Convergents and Semiconvergents in Pythagorean Tuning, Axioms (2025) Vol. 14, No. 9, 707. See Appendix A.2.

Edward G. Dunne, Pianos and Continued Fractions

Terence Jackson and Keith Matthews, "On Shanks' Algorithm for Computing the Continued Fraction of log_b a" , Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.7

Terence H. Jackson and Keith R. Matthews, The 1000 partial quotients of log_2(3)

Dave Rusin, Why 12 tones per octave? [Broken link]

Dave Rusin, Why 12 tones per octave? [Cached copy]

Example

log_2(3) = 1.5849625007211561814537389439...

Maple

Digits := 200: convert(evalf( log(3)/log(2) ), confrac);

Mathematica

ContinuedFraction[Log[2, 3], 120] (* Harvey P. Dale, Oct 24 2011 *)

Crossrefs

Cf. A005663, A005664, A020857 (decimal expansion).

Sequence in context: A370777 A088177 A335917 * A096226 A155980 A309531

Adjacent sequences: A028504 A028505 A028506 * A028508 A028509 A028510

Keyword

nonn,cofr,nice,easy

Author

Tony Smith (tsmith(AT)innerx.net)

Extensions

More terms from James Sellers, Sep 16 2000

Offset changed by Andrew Howroyd, Aug 07 2024

Status

approved