A005663 - OEIS

A005663

Numerators of convergents to log_2(3) = log(3)/log(2).
(Formerly M0883)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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

R. K. Guy, Letter to N. J. A. Sloane, 1977

Eric Weisstein's World of Music, Comma of Pythagoras

EXAMPLE

log_2(3) = 1.5849625007211561814537389439...

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A005664, A028507, A020857.

Sequence in context: A303835 A007999 A006609 * A112834 A042697 A042905

Adjacent sequences: A005660 A005661 A005662 * A005664 A005665 A005666

KEYWORD

frac,easy,nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Sep 16 2000

STATUS

approved