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 A267316 Decimal expansion of the Dirichlet eta function at 5. 5
 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 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+1)/k^5 = (15*zeta(5))/16. Equals Lim_{n -> infinity} A136676(n)/A334604(n). - Petros Hadjicostas, May 07 2020 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 range(1, 10000): s += -((-1)^i/((i)^5)) print(s) # Terry D. Grant, Aug 05, 2016 CROSSREFS Cf. A002162 (value at 1), A013663, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A136676, A334604. Sequence in context: A083995 A195357 A328968 * 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 September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)