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A269444 Continued fraction expansion of the Dirichlet eta function at 3. 0
0, 1, 9, 6, 2, 1, 1, 1, 1, 1, 1, 6, 1, 4, 1, 7, 2, 1, 1, 1, 2, 91, 32, 1, 1, 6, 23, 1, 1, 1, 1, 2, 9, 1, 2, 1, 1, 5, 1, 1, 37, 12, 1, 12, 3, 2, 87, 1, 4, 2, 2, 2, 320, 1, 7, 1, 2, 6, 3, 1, 6, 4, 1, 4, 2, 1, 69, 1, 4, 3, 3, 1, 14, 3, 1, 3, 1, 10, 2, 694, 2, 4, 21, 1, 1, 1, 3, 3, 10, 2, 1, 2, 2, 1, 3, 5, 1, 3, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction expansion of Sum_{k>=1} (-1)^(k - 1)/k^3 = (3*zeta(3))/4 = 0.901542677369695714...

LINKS

Table of n, a(n) for n=0..99.

OEIS Wiki, Euler's alternating zeta function

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Wikipedia, Dirichlet Eta Function

Index entries for continued fractions for constants

EXAMPLE

1/1^3 - 1/2^3 + 1/3^3 - 1/4^3 + 1/5^3 - 1/6^3 +... = 1/(1 + 1/(9 + 1/(6 + 1/(2 + 1/(1 + 1/(1 + 1/...)))))).

MATHEMATICA

ContinuedFraction[(3 Zeta[3])/4, 100]

CROSSREFS

Cf. A013631, A197070.

Sequence in context: A064230 A286331 A089479 * A199431 A154899 A011219

Adjacent sequences:  A269441 A269442 A269443 * A269445 A269446 A269447

KEYWORD

nonn,cofr

AUTHOR

Ilya Gutkovskiy, Feb 26 2016

STATUS

approved

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Last modified November 21 11:43 EST 2018. Contains 317447 sequences. (Running on oeis4.)