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A188627
Continued fraction of e+sqrt(e^2-1).
3
5, 4, 15, 6, 1, 13, 2, 1, 1, 21, 3, 2, 16, 1, 4, 1, 1, 157, 1, 9, 1, 3, 1, 5, 1, 2, 1, 3, 1, 1, 1, 1, 11, 1, 1, 22, 1, 9, 1, 1, 1, 1, 12, 1, 7, 6, 1, 3, 2, 8, 1, 1, 1, 1, 4, 2, 3, 1, 10, 17, 1, 2, 1, 5, 8, 1, 2, 1, 6, 1, 12, 1, 39, 16, 14, 1, 46, 72, 16, 3, 1, 1, 5, 2, 1, 5, 2, 1, 10, 4, 2, 2, 3, 2, 1, 3, 2, 2, 27, 10, 4, 2, 8, 1, 2, 6, 3, 945, 1, 1, 106, 1, 1, 3, 1, 2, 6, 1, 1, 2
OFFSET
0,1
LINKS
EXAMPLE
e+sqrt(e^2-1) = [5, 4, 15, 6, 1, 13, 2, 1, 1, 21, 3, 2, 16, 1, ...]
MATHEMATICA
r = 2 E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A188739 *)
ContinuedFraction[t, 120] (* A188627 *)
PROG
(PARI) default(realprecision, 100); contfrac(exp(1) + sqrt(exp(2) - 1)) \\ G. C. Greubel, Nov 01 2018
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(Exp(1) + Sqrt(Exp(2) - 1)); // G. C. Greubel, Nov 01 2018
CROSSREFS
Cf. A188739 (decimal expansion).
Sequence in context: A133178 A377626 A154225 * A203976 A213566 A143129
KEYWORD
nonn,cofr
AUTHOR
Clark Kimberling, Apr 11 2011
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 08 2024
STATUS
approved