

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
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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. 1556.
S. R. Finch, "Mathematical Constants", Cambridge, pp. 423428.
H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, 1948, pp. 356358, 367


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
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. A099287, A108088, A111188.
Cf. A225435, A225436 (numerators and denominators of convergents to c.f.).
Sequence in context: A166199 A324860 A008566 * A168464 A059688 A072996
Adjacent sequences: A111126 A111127 A111128 * A111130 A111131 A111132


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



