A111129 Decimal expansion of the continued fraction 1+1/(1+2/(1+3/(1+4/(1+5/(1+...))))).

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

Offset: 1

Author

N. J. A. Sloane, based on correspondence from Tom Raes (tommy1729(AT)hotmail.com) and Steven Finch, Sep 22 2005

Keywords

• nonn
• cons

Examples

			1.52513527616098120908909053639057871330711636492060333554631394242...
		

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

• 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

Crossrefs

Cf. A099287, A108088, A111188.

Cf. A225435, A225436 (numerators and denominators of convergents to c.f.).

Programs

Mathematica

RealDigits[1/(Sqrt[Pi*E/2]*Erfc[1/Sqrt[2]]), 10, 111][[1]]

PARI

1/(sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2))) \\ G. C. Greubel, Jan 24 2017

Formula

Equals the reciprocal of sqrt(pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function.

Extensions

More terms from Robert G. Wilson v and Hans Havermann, Oct 17 2005

Definition corrected by Steven Finch, Feb 05 2009