A005664 Denominators of convergents to log_2 3.

1, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867, 79335, 111202, 190537, 10590737, 10781274, 53715833, 171928773, 225644606, 397573379, 6189245291, 6586818670, 65470613321, 137528045312, 753110839881, 5409303924479, 6162414764360

Offset: 0

Author

N. J. A. Sloane, R. K. Guy

Keywords

• nonn
• frac
• easy

Examples

			log_2 3 = 1.5849625007211561814537389439...
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Oliver K. Clay, The Long Search for Collatz Counterexamples, J. Humanistic Math. (2023) Vol. 13, No. 2, 199-227. See p. 205.
• R. E. Crandall, On the 3x+1 problem, Math. Comp., 32 (1978) 1281-1292.
• E. G. Dunne, Pianos and Continued Fractions
• R. K. Guy, Letter to N. J. A. Sloane, 1977
• David Ryan, An algorithm to assign musical prime commas to every prime number and construct a universal and compact free Just Intonation musical notation, Preprint, arXiv preprint arXiv:1612.01860 [cs.SD], 2016.
• Eric Weisstein's World of Music, Comma of Pythagoras

Crossrefs

Cf. A005663, A028507, A020857.

Programs

Mathematica

Convergents[Log[2, 3], 30] // Denominator (* Jean-François Alcover, Dec 12 2016 *)

PARI

a(n) = component(component(contfracpnqn(contfrac(log(3)/log(2), n)), 1), 2) \\ Michel Marcus, May 20 2013

Extensions

More terms from James Sellers, Sep 16 2000