login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111129 Decimal expansion of the continued fraction 1+1/(1+2/(1+3/(1+4/(1+5/(1+...))))). 9
1, 5, 2, 5, 1, 3, 5, 2, 7, 6, 1, 6, 0, 9, 8, 1, 2, 0, 9, 0, 8, 9, 0, 9, 0, 5, 3, 6, 3, 9, 0, 5, 7, 8, 7, 1, 3, 3, 0, 7, 1, 1, 6, 3, 6, 4, 9, 2, 0, 6, 0, 3, 3, 3, 5, 5, 4, 6, 3, 1, 3, 9, 4, 2, 4, 2, 7, 2, 2, 6, 9, 2, 5, 5, 0, 7, 9, 5, 0, 3, 1, 6, 8, 7, 0, 2, 2, 8, 0, 1, 1, 8, 2, 6, 7, 2, 1, 1, 6, 5, 5, 2, 1, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
B. C. Berndt, Y.-S. Choi and S.-Y. Kang, The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society, Continued Fractions: From Analytic Number Theory to Constructive Approximation, ed. B. C. Berndt and F. Gesztesy, Amer. Math. Soc., 1999, pp. 15-56.
S. R. Finch, "Mathematical Constants", Cambridge, pp. 423-428.
H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, 1948, pp. 356-358, 367
LINKS
Eric Weisstein's World of Mathematics, Continued Fraction Constants
Eric Weisstein's World of Mathematics, Generalized Continued Fraction
FORMULA
Equals the reciprocal of sqrt(pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function.
EXAMPLE
1.52513527616098120908909053639057871330711636492060333554631394242...
MATHEMATICA
RealDigits[1/(Sqrt[Pi*E/2]*Erfc[1/Sqrt[2]]), 10, 111][[1]]
PROG
(PARI) 1/(sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2))) \\ G. C. Greubel, Jan 24 2017
CROSSREFS
Cf. A225435, A225436 (numerators and denominators of convergents to c.f.).
Sequence in context: A166199 A324860 A008566 * A168464 A059688 A072996
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, based on correspondence from Tom Raes (tommy1729(AT)hotmail.com) and Steven Finch, Sep 22 2005
EXTENSIONS
More terms from Robert G. Wilson v and Hans Havermann, Oct 17 2005
Definition corrected by Steven Finch, Feb 05 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 02:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)