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
Examples
log_2(3) = 1.5849625007211561814537389439...
Links
- T. D. Noe, Table of n, a(n) for n = 0..9999
- E. 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
- T. H. Jackson & K. 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]
Programs
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Maple
Digits := 200: convert(evalf( log(3)/log(2) ),confrac);
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Mathematica
ContinuedFraction[Log[2,3],120] (* Harvey P. Dale, Oct 24 2011 *)
Extensions
More terms from James Sellers, Sep 16 2000
Offset changed by Andrew Howroyd, Aug 07 2024