A269482 Continued fraction expansion of the Dirichlet eta function at 5.

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

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 A350936 A297875

Adjacent sequences: A269479 A269480 A269481 * A269483 A269484 A269485

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Feb 27 2016

Status

approved