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A269482 Continued fraction expansion of the Dirichlet eta function at 5. 0
0, 1, 34, 1, 6, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 35, 3, 1, 5, 4, 1, 2, 2, 1, 4, 1, 1, 1, 2, 10, 2, 1, 6, 9, 23, 1, 5, 1, 1, 1, 1, 1, 2, 1, 3, 4, 1, 2, 1, 1, 2, 2, 1, 1, 5, 4, 7, 1, 1, 1, 1, 2, 2, 1, 4, 1, 1, 2, 8, 3, 2, 1, 3, 1, 5, 356, 2, 57, 6, 1, 6, 1, 1, 31, 1, 5, 1, 1, 477, 1, 9, 7, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^5 = (15*zeta(5))/16 = 0.9721197704469093...

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

1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 +... = 1/(1 + 1/(34 + 1/(1 + 1/(6 + 1/(1 + 1/(1 + 1/...)))))).

MATHEMATICA

ContinuedFraction[(15 Zeta[5])/16, 100]

CROSSREFS

Cf. A013681, A267316.

Sequence in context: A022070 A123301 A328913 * A037933 A297875 A298138

Adjacent sequences:  A269479 A269480 A269481 * A269483 A269484 A269485

KEYWORD

nonn,cofr

AUTHOR

Ilya Gutkovskiy, Feb 27 2016

STATUS

approved

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Last modified October 23 10:17 EDT 2021. Contains 348211 sequences. (Running on oeis4.)