A251734 -id:A251734 - cp's OEIS frontend

A251735 Decimal expansion of Sum_{n>=1} (-1)^(n+1)/n^(1/3).

5, 7, 1, 7, 5, 2, 8, 3, 3, 8, 2, 5, 2, 7, 7, 6, 6, 4, 9, 3, 6, 4, 7, 5, 6, 8, 1, 1, 3, 6, 0, 3, 2, 6, 5, 5, 2, 4, 3, 1, 4, 8, 1, 5, 7, 4, 7, 3, 2, 5, 4, 1, 1, 5, 8, 0, 6, 1, 4, 7, 5, 0, 8, 2, 8, 0, 3, 1, 8, 4, 9, 1, 1, 9, 3, 9, 9, 3

Offset: 0

R. J. Mathar, Dec 07 2014

Cubic root analog of A113024.

			0.57175283382527766493...

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A005480, A113024, A251734.

Maple
```
Zeta(1/3)*(1-root[3](4)) ; evalf(%) ;
```

RealDigits[-Zeta[1/3]*(4^(1/3) - 1), 10, 100][[1]] (* G. C. Greubel, Apr 15 2018 *)

-zeta(1/3)*(4^(1/3)-1) \\ Charles R Greathouse IV, Apr 20 2016

Equals 1 - 1/A002580 + 1/A002581 - 1/A005480 + ... = A251734 *(1 - A005480).

A385423 Decimal expansion of the absolute value of zeta(1/5).

Original entry on oeis.org

7, 3, 3, 9, 2, 0, 9, 2, 4, 8, 9, 6, 3, 4, 0, 5, 9, 2, 2, 4, 3, 8, 0, 9, 6, 1, 3, 7, 5, 5, 1, 3, 6, 8, 6, 6, 6, 4, 9, 1, 2, 8, 6, 9, 3, 8, 3, 2, 3, 1, 5, 3, 3, 6, 4, 4, 3, 9, 2, 6, 2, 4, 0, 6, 0, 9, 1, 6, 4, 9, 7, 8, 7, 4, 4, 6, 4, 1, 0, 8, 2, 5, 9, 3, 8, 5, 7, 5, 4, 9, 4, 3, 7, 9, 8, 5, 7, 3, 7, 6, 2, 6, 9, 7, 9

Offset: 0

Artur Jasinski, Jul 26 2025

			0.7339209248963405922438096137551368666491286938...

Cf. A251734, A386590.

evalf(abs(Zeta(1/5)), 120);  # Alois P. Heinz, Jul 26 2025

Mathematica
```
RealDigits[-Zeta[1/5], 10, 105][[1]]
```

Equals (1/(2^(4/5)-1))*Sum_{k>=1} (-1)^(k+1)/k^(1/5).

A386590 Decimal expansion of the absolute value of zeta(1/4).

Original entry on oeis.org

8, 1, 3, 2, 7, 8, 4, 0, 5, 2, 6, 1, 8, 9, 1, 6, 5, 6, 5, 2, 1, 4, 4, 7, 8, 2, 0, 0, 7, 3, 5, 2, 5, 5, 7, 4, 4, 8, 1, 5, 7, 0, 5, 2, 4, 5, 2, 9, 0, 0, 5, 8, 4, 2, 6, 0, 5, 0, 6, 6, 9, 7, 3, 4, 4, 2, 0, 1, 7, 8, 2, 9, 7, 2, 4, 4, 1, 0, 2, 1, 7, 1, 0, 1, 9, 9, 1, 4, 6, 5, 2, 2, 9, 5, 4, 0, 3, 3, 7, 0, 9, 8, 3, 8, 5

Offset: 0

Artur Jasinski, Jul 26 2025

			0.81327840526189165652144782007352557448157...

Cf. A251734, A385423.

evalf(abs(Zeta(1/4)), 120);  # Alois P. Heinz, Jul 26 2025

Mathematica
```
RealDigits[-Zeta[1/4], 10, 105][[1]]
```

-zeta(1/4) \\ Stefano Spezia, Aug 03 2025

Sum_{k>=1} (-1)^(k+1)/k^(1/4) = |Zeta(1/4)| * (2^(3/4)-1) = this * (A011006 -1).

A091558 Decimal expansion of zeta(Gamma^2).

Original entry on oeis.org

9, 7, 3, 0, 2, 2, 8, 8, 9, 0, 2, 5, 8, 9, 5, 6, 1, 4, 6, 7, 0, 1, 8, 4, 2, 8, 9, 5, 1, 5, 4, 3, 0, 6, 5, 6, 6, 4, 1, 7, 5, 8, 5, 4, 1, 1, 3, 8, 0, 4, 2, 8, 2, 7, 0, 0, 7, 7, 5, 5, 0, 8, 7, 4, 8, 1, 8, 8, 7, 5, 2, 2, 9, 1, 4, 7, 8, 7, 3, 1, 3, 3, 6, 7, 5, 0, 4, 2, 0, 6, 0, 8, 5, 6, 6, 3, 6, 9, 0, 4

Offset: 0

Jon Perry, Mar 04 2004

			zeta(gamma^2)=-0.973022889025895614670184289515430656641758541138042827...

Cf. A155969, A251734.

Zeta(gamma^2) ; evalf(%) # R. J. Mathar, Aug 27 2024

RealDigits[Zeta[EulerGamma^2],10,120][[1]] (* Harvey P. Dale, Nov 09 2017 *)

PARI
```
zeta(Euler^2)
```

cp's OEIS Frontend

A251735 Decimal expansion of Sum_{n>=1} (-1)^(n+1)/n^(1/3).

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A385423 Decimal expansion of the absolute value of zeta(1/5).

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Maple

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A386590 Decimal expansion of the absolute value of zeta(1/4).

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Maple

Mathematica

PARI

Formula

A091558 Decimal expansion of zeta(Gamma^2).

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Maple

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