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A001204 Continued fraction for e^2.
(Formerly M4322 N1811)
8
7, 2, 1, 1, 3, 18, 5, 1, 1, 6, 30, 8, 1, 1, 9, 42, 11, 1, 1, 12, 54, 14, 1, 1, 15, 66, 17, 1, 1, 18, 78, 20, 1, 1, 21, 90, 23, 1, 1, 24, 102, 26, 1, 1, 27, 114, 29, 1, 1, 30, 126, 32, 1, 1, 33, 138, 35, 1, 1, 36, 150, 38, 1, 1, 39, 162, 41, 1, 1, 42, 174, 44, 1, 1, 45, 186, 47, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

O. Perron, Die Lehre von den Kettenbr├╝chen, 2nd ed., Teubner, Leipzig, 1929, p. 138.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

LINKS

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

K. Matthews, Finding the continued fraction of e^(l/m)

G. Xiao, Contfrac

Index entries for continued fractions for constants

FORMULA

G.f.: (x^10-x^8-x^7+x^6+4x^5+3x^4+x^3+x^2+2x+7)/(x^5-1)^2. - Ralf Stephan, Mar 23 2003

For n>0, a(5n)=12n+6, a(5n+1)=3n+2, a(5n+2)=a(5n+3)=1 and a(5n+4)=3n+3. - Dean Hickerson, Mar 25 2003

EXAMPLE

7.389056098930650227230427460... = 7 + 1/(2 + 1/(1 + 1/(1 + 1/(3 + ...)))) [Harry J. Smith, Apr 30 2009]

MATHEMATICA

ContinuedFraction[ E^2, 100]

PROG

(PARI) contfrac(exp(2))

(PARI) { allocatemem(932245000); default(realprecision, 95000); x=contfrac(exp(2)); for (n=1, 20001, write("b001204.txt", n-1, " ", x[n])); } [Harry J. Smith, Apr 30 2009]

CROSSREFS

Cf. A003417, A005131, A058282.

Sequence in context: A153589 A010505 A020844 * A177969 A021585 A103713

Adjacent sequences:  A001201 A001202 A001203 * A001205 A001206 A001207

KEYWORD

easy,nonn,cofr,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Robert G. Wilson v, Dec 07 2000

STATUS

approved

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Last modified October 21 23:13 EDT 2014. Contains 248381 sequences.