A058282 Continued fraction for e^3.

20, 11, 1, 2, 4, 3, 1, 5, 1, 2, 16, 1, 1, 16, 2, 13, 14, 4, 6, 2, 1, 1, 2, 2, 2, 3, 5, 1, 3, 1, 1, 68, 7, 5, 1, 4, 2, 1, 1, 1, 1, 1, 1, 7, 3, 1, 6, 1, 2, 5, 4, 7, 2, 1, 3, 2, 2, 1, 2, 1, 4, 1, 1, 13, 1, 1, 2, 1, 1, 1, 1, 3, 7, 11, 18, 54, 1, 2, 2, 2, 1, 1, 6, 2, 2, 46, 2, 189, 1, 24, 1, 8, 13, 4, 1, 1

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

K. Matthews, Finding the continued fraction of e^(l/m) ["... there is no known formula for the partial quotients of the continued fraction expansion of e^3, or more generally e^(l/m) with l distinct from 1,2 and gcd(l,m)=1..."]

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

20.085536923187667740928529... = 20 + 1/(11 + 1/(1 + 1/(2 + 1/(4 + ...)))). - Harry J. Smith, Apr 30 2009

Maple

with(numtheory); Digits:=200: cf:=convert(evalf( exp(3)), confrac); # N. J. A. Sloane, Sep 05 2012

Mathematica

ContinuedFraction[ E^3, 100]

Prog

(PARI) contfrac(exp(1)^3)
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(3)); for (n=1, 20001, write("b058282.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 30 2009

Crossrefs

Cf. A001204, A003417, A005131.

Sequence in context: A033966 A033340 A040383 * A298208 A247337 A071160

Adjacent sequences: A058279 A058280 A058281 * A058283 A058284 A058285

Keyword

cofr,nonn,easy

Author

Robert G. Wilson v, Dec 07 2000

Extensions

More terms from Jason Earls, Jul 10 2001

Status

approved