A005663 Numerators of convergents to log_2(3) = log(3)/log(2).

1, 2, 3, 8, 19, 65, 84, 485, 1054, 24727, 50508, 125743, 176251, 301994, 16785921, 17087915, 85137581, 272500658, 357638239, 630138897, 9809721694, 10439860591, 103768467013, 217976794617, 1193652440098, 8573543875303

Offset: 0

Author

N. J. A. Sloane

Keywords

• frac
• easy
• nonn

Examples

			log_2(3) = 1.5849625007211561814537389439...
		

References

• R. K. Guy, personal communication.
• 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
• R. E. Crandall, On the 3x+1 problem, Math. Comp., 32 (1978) 1281-1292.
• E. G. Dunne, Pianos and Continued Fractions
• E. G. Dunne, Pianos and Continued Fractions
• R. K. Guy, Letter to N. J. A. Sloane, 1977
• Eric Weisstein's World of Music, Comma of Pythagoras

Crossrefs

Cf. A005664, A028507, A020857.

Programs

Mathematica

Numerator[Convergents[Log[2,3],30]] (* Harvey P. Dale, Sep 10 2015 *)

PARI

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

Extensions

More terms from James Sellers, Sep 16 2000