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A058281 Continued fraction for square root of e. 9
1, 1, 1, 1, 5, 1, 1, 9, 1, 1, 13, 1, 1, 17, 1, 1, 21, 1, 1, 25, 1, 1, 29, 1, 1, 33, 1, 1, 37, 1, 1, 41, 1, 1, 45, 1, 1, 49, 1, 1, 53, 1, 1, 57, 1, 1, 61, 1, 1, 65, 1, 1, 69, 1, 1, 73, 1, 1, 77, 1, 1, 81, 1, 1, 85, 1, 1, 89, 1, 1, 93, 1, 1, 97, 1, 1, 101, 1, 1, 105, 1, 1, 109, 1, 1, 113, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

sqrt(e) = 1.64872127070012814684865078781416357165377610071014801157507... - Harry J. Smith, May 01 2009

LINKS

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

D. H. Lehmer, Continued fractions containing arithmetic progressions, Scripta Mathematica, 29 (1973): 17-24. [Annotated copy of offprint]

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

T. J. Osler, A proof of the continued fraction expansion of e^(1/M), Amer. Math. Monthly, 113 (No. 1, 2006), 62-66.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

FORMULA

a(3k+1) = 4k+1, a(i) = 1 otherwise.

G.f.: -(x^2-x+1)*(x^3-2*x^2-2*x-1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, Jun 24 2013

EXAMPLE

sqrt(e) = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(5 + ...)))). - Harry J. Smith, May 01 2009

MATHEMATICA

ContinuedFraction[ Sqrt[E], 100]

PROG

(PARI) contfrac(sqrt(exp(1)))

(PARI) { allocatemem(932245000); default(realprecision, 60000); x=contfrac(sqrt(exp(1))); for (n=1, 20001, write("b058281.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 01 2009

CROSSREFS

Cf. A004766, A016813.

Cf. A019774 for decimal expansion of sqrt(e).

Sequence in context: A054110 A132048 A141398 * A046583 A046579 A153108

Adjacent sequences:  A058278 A058279 A058280 * A058282 A058283 A058284

KEYWORD

cofr,nonn,easy,nice

AUTHOR

Robert G. Wilson v, Dec 07 2000

EXTENSIONS

More terms from Jason Earls, Jul 10 2001

STATUS

approved

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Last modified February 20 01:06 EST 2018. Contains 299357 sequences. (Running on oeis4.)