A005664 Denominators of convergents to log_2 3. (Formerly M1428)

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

0,3

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

Example

log_2 3 = 1.5849625007211561814537389439...

Mathematica

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

Prog

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

Crossrefs

Cf. A005663, A028507, A020857.

Sequence in context: A054581 A203151 A140440 * A364761 A009739 A062272

Adjacent sequences: A005661 A005662 A005663 * A005665 A005666 A005667

Keyword

nonn,frac,easy

Author

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

Extensions

More terms from James A. Sellers, Sep 16 2000

Status

approved