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A267316 Decimal expansion of the Dirichlet eta function at 5. 3
9, 7, 2, 1, 1, 9, 7, 7, 0, 4, 4, 6, 9, 0, 9, 3, 0, 5, 9, 3, 5, 6, 5, 5, 1, 4, 3, 5, 5, 3, 4, 6, 9, 5, 3, 2, 5, 5, 3, 5, 1, 3, 3, 6, 2, 0, 3, 3, 0, 4, 3, 2, 6, 1, 2, 2, 5, 8, 0, 5, 6, 3, 5, 5, 3, 4, 8, 1, 5, 8, 6, 5, 4, 2, 4, 6, 3, 8, 8, 9, 1, 7, 7, 5, 0, 4, 0, 4, 1, 2, 3, 9, 7, 3, 1, 2, 5, 0, 2, 8, 5, 5, 8, 9, 4, 0, 7, 0, 1, 2, 4, 8, 9, 6, 8, 2, 0, 9, 7, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..119.

OEIS Wiki, Euler's alternating zeta function

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Wikipedia, Dirichlet Eta Function

FORMULA

Equals Sum_{k > 0} - (-1)^k/k^5 = (15*zeta(5))/16.

EXAMPLE

1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 + ... = 0.972119770446909305935655143553469532553513362...

MATHEMATICA

RealDigits[(15 Zeta[5])/16, 10, 120][[1]]

PROG

(PARI) 15*zeta(5)/16 \\ Michel Marcus, Feb 01 2016

(Sage) s = RLF(0); s

RealField(110)(s)

for i in xrange(1, 10000): s += -((-1)^i/((i)^5))

print s # Terry D. Grant, Aug 05, 2016

CROSSREFS

Cf. A002162 (decimal expansion of value at 1), A072691 (value at 2), A197070 (value at 3), A267315 (value at 4).

Sequence in context: A069611 A083995 A195357 * A021511 A029688 A155792

Adjacent sequences:  A267313 A267314 A267315 * A267317 A267318 A267319

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Jan 13 2016

STATUS

approved

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Last modified October 20 17:47 EDT 2018. Contains 316396 sequences. (Running on oeis4.)