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 A058281 Continued fraction for square root of e. 10
 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 E.g.f.: exp(-x/2)*(exp(3*x/2)*(5 + 4*x) + (4 + 8*x)*cos(sqrt(3)*x/2) - 4*sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, May 05 2022 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 September 30 09:22 EDT 2023. Contains 365784 sequences. (Running on oeis4.)