A365116 -id:A365116 - cp's OEIS frontend

A113014 Decimal expansion of value of the continued fraction 1/(2+3/(4+5/(6+7/....

3, 7, 9, 7, 3, 1, 9, 5, 4, 7, 4, 0, 9, 9, 5, 6, 3, 2, 8, 0, 2, 1, 0, 6, 2, 5, 3, 6, 3, 4, 7, 5, 5, 3, 8, 1, 6, 1, 2, 5, 9, 4, 1, 6, 0, 3, 5, 9, 0, 8, 1, 2, 5, 3, 1, 5, 2, 6, 4, 3, 3, 4, 4, 9, 4, 4, 8, 8, 0, 5, 2, 5, 3, 7, 3, 6, 3, 5, 6, 7, 3, 8, 3, 1, 7, 4, 4, 4, 8, 3, 2, 3, 0, 7, 1, 5, 4, 8, 1, 7, 4, 8, 3, 4, 0

Offset: 0

T. D. Noe, Oct 10 2005

This fraction equals sqrt(2e/Pi)/erfi(1/sqrt(2)) - 1. - Robert Israel, Aug 29 2007

			0.3797319547409956328...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Sci.math, Continued Fractions.

Cf. A365105, A365116.

n=150; s=n; While[n-2>=0, s=n-2 + (n-1)/s; n=n-2]; RealDigits[N[s, 120]][[1]]
RealDigits[N[Sqrt[2E/Pi]/Erfi[1/Sqrt[2]]-1,120]][[1]] (* T. D. Noe, Oct 06 2008 *)

{Erfi(z) = -I*(1.0-erfc(I*z))};
real(sqrt(2*exp(1)/Pi)/Erfi(1/sqrt(2)) - 1) \\ G. C. Greubel, Apr 09 2018

Sci.math link from Bhushit Joshipura (joshipura(AT)gmail.com), Jul 15 2008

A365105 Continued fraction expansion of 1/(2+3/(4+5/(6+7/(...)))) = A113014.

Original entry on oeis.org

0, 2, 1, 1, 1, 2, 1, 2, 10, 2, 2, 66, 1, 1, 13, 66, 9, 5, 8, 1, 9, 1, 1, 1, 5, 2, 2, 3, 1, 1, 1, 16, 99, 6, 1, 5, 1, 2, 1, 55, 2, 2, 1, 1, 6, 4, 1, 1, 1, 40, 1, 1, 1, 6, 14, 7, 9, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2, 7, 12, 1, 2, 2, 1, 4, 2, 4, 2, 1, 3, 2, 1, 10, 7, 1, 4, 1, 119, 1, 1, 1, 3, 5, 2, 12, 1

Offset: 0

Rok Cestnik, Aug 21 2023

A113014 is defined by a generalized continued fraction and the expansion here is its simple continued fraction.

			1/(2+1/(1+1/(1+1/(1+1/(2+1/(...)))))) = 1/(2+3/(4+5/(6+7/(...)))).

Cf. A113014, A365116.

A365105 = ContinuedFraction[Sqrt[2*E/Pi]/Erfi[1/Sqrt[2]]-1,#]&;

cp's OEIS Frontend

A113014 Decimal expansion of value of the continued fraction 1/(2+3/(4+5/(6+7/....

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