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A269443 Continued fraction expansion of the Dirichlet eta function at 2. 0
0, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 4, 1, 1, 1, 1, 1, 1, 4, 1, 6, 3, 7, 1, 7, 3, 3, 2, 4, 2, 2, 1, 1, 2, 1, 1, 3, 2, 1, 5, 1, 3, 1, 2, 1, 1, 13, 40, 1, 1, 1, 48, 211, 4, 91, 1, 16, 9, 1, 10, 8, 2, 4, 1, 2, 3, 2, 1, 1, 13, 3, 1, 2, 2, 1, 3, 1, 18, 2, 1, 1, 1, 5, 3, 7, 1, 1, 21, 1, 6, 4, 1, 1, 2, 1, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction expansion of Sum_{k>=1} (-1)^(k-1)/k^2 = Zeta(2)/2 = Pi^2/12 = 0.8224670334241132182362...

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

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

MATHEMATICA

ContinuedFraction[Pi^2/12, 100]

PROG

(PARI) contfrac(Pi^2/12) \\ Michel Marcus, Feb 26 2016

CROSSREFS

Cf. A013679, A072691.

Sequence in context: A265143 A181873 A229293 * A039927 A073802 A132157

Adjacent sequences:  A269440 A269441 A269442 * A269444 A269445 A269446

KEYWORD

nonn,cofr

AUTHOR

Ilya Gutkovskiy, Feb 26 2016

STATUS

approved

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Last modified October 22 14:41 EDT 2018. Contains 316486 sequences. (Running on oeis4.)