A108088 Decimal expansion of 1/(1+1/(1+2/(1+3/(1+4/(1+5/(1+...)))))).
6, 5, 5, 6, 7, 9, 5, 4, 2, 4, 1, 8, 7, 9, 8, 4, 7, 1, 5, 4, 3, 8, 7, 1, 2, 3, 0, 7, 3, 0, 8, 1, 1, 2, 8, 3, 3, 9, 9, 2, 8, 2, 3, 3, 2, 8, 7, 0, 4, 6, 2, 0, 2, 8, 0, 5, 3, 6, 8, 6, 1, 5, 8, 7, 3, 4, 1, 9, 7, 1, 6, 5, 7, 6, 6, 3, 1, 0, 5, 8, 9, 0, 6, 5, 8, 5, 0, 9, 5
Offset: 0
Examples
0.6556795424187984715438712307308112833992823328704...
References
- S. R. Finch, "Mathematical Constants", Cambridge, pp. 423-428.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
Crossrefs
Cf. A111129.
Programs
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Mathematica
RealDigits[Sqrt[Pi*E/2]*Erfc[1/Sqrt[2]], 10, 111][[1]]
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PARI
sqrt(Pi*exp(1)/2)*erfc(1/sqrt(2)) \\ G. C. Greubel, Feb 03 2017
Formula
Equals sqrt(Pi*e/2)*erfc(1/sqrt(2)), where erfc is the complementary error function. - Daniel Forgues, Apr 14 2011
Also equals Integral_{-infinity..infinity} (1/sqrt(2*Pi))*exp(-x^2/2)/(1+x^2) dx, where the integrand is normal PDF times Cauchy PDF. - Jean-François Alcover, Apr 28 2015
Comments