A092731 -id:A092731 - cp's OEIS frontend

A222074 Decimal expansion of (1/1920)*Pi^5.

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

Offset: 0

N. J. A. Sloane, Feb 10 2013

			.15938525249233409024101109898095604504182328470212239091327...

Index entries for transcendental numbers

Related constants: A092731, A222073, A222075.

RealDigits[Pi^5/1920,10,120][[1]] (* Harvey P. Dale, Oct 03 2013 *)

Pi^5/1920 \\ Charles R Greathouse IV, Oct 31 2014

Edited by Andrey Zabolotskiy, Dec 29 2023

A222075 Decimal expansion of (64/10395)*Pi^5.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Feb 10 2013

Volume of the 11-dimensional unit ball.

			1.8841038793899002413482870459624703044482198387875708894106...

Index entries for transcendental numbers.

Related constants: A092731, A276023, A222073, A222074.

RealDigits[64*Pi^5/10395, 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)

fpprec : 100$ev((64/10395)*%pi^5)$bfloat(%); /* Martin Ettl, Feb 12 2013 */

64*Pi^5/10395 \\ Charles R Greathouse IV, Oct 31 2014

Edited by Andrey Zabolotskiy, Dec 29 2023

A309926 Decimal expansion of Pi^5/Zeta(5).

Original entry on oeis.org

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

Offset: 3

Seiichi Manyama, Aug 23 2019

Index entries for zeta function.

Cf. A013663, A092731, A308637.

RealDigits[Pi^5/Zeta[5], 10, 100][[1]] (* Amiram Eldar, Aug 24 2019 *)

PARI
```
Pi^5/zeta(5)
```

Pi^5/Zeta(5) = A092731/A013663.

More terms from Amiram Eldar, Aug 24 2019

A060302 Decimal expansion of (Pi^4 + Pi^5)^(1/6).

Original entry on oeis.org

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

Offset: 1

Jason Earls, Mar 26 2001

Approximation to e, accurate to 7 decimal places.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for transcendental numbers.

Cf. A001113, A000796, A092425, A092731.

RealDigits[Surd[Pi^4 + Pi^5, 6], 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

default(realprecision, 20080); x=(Pi^4 + Pi^5)^(1/6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b060302.txt", n, " ", d)); \\ Harry J. Smith, Jul 03 2009

A378408 Decimal expansion of Pi^5/90.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 25 2024

See Penn link for a geometric interpretation.

			3.4002187198364605918082367782603956275588967403119...

Amiram Eldar, Illustration.
Michael Penn, A twist on a classic circle problem, YouTube video, 2024.
Index entries for constants related to zeta.
Index entries for transcendental numbers.

Cf. A000796, A013662, A092731, A279037.

Mathematica
```
First[RealDigits[Pi^5/90, 10, 100]]
```

Pi^5/90 \\ Charles R Greathouse IV, Nov 27 2024

Equals Pi*Sum_{k >= 1} 1/k^4 = Pi*zeta(4) = A000796*A013662.

Equals A092731/90.

A194656 Decimal expansion of (2Pi^5log(2) - 30Pi^3zeta(3) + 225Pizeta(5))/320.

Original entry on oeis.org

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

Offset: 0

Seiichi Kirikami, Sep 01 2011

The absolute value of the integral{x=0..Pi/2} x^4*log(sin(x )) dx or(d^4/da^4(integral {x=0..Pi/2} cos(ax)*log(sin(x )) dx)) at a=0. The absolute value of m=2 of (-1)^(m+1)*(sum {n=1..infinity} (limit {a -> 0} (d^(2m)/da^(2m)(sin((a+2n)*Pi/2)/n/(a+2n)))))-(Pi/2)^(2m+1)*log(2)/(2m+1). - Seiichi Kirikami and Peter J. C. Moses, Sep 01 2011

			0.12204729588592872163...

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 1.441.2

Cf. A173623, A173624, A193716, A193717.

RealDigits[ N[Pi (2 Pi^4*Log[2]-30 Pi^2*Zeta[3]+225 Zeta[5])/320, 150]][[1]]

Equals (2*A092731*A002162-30*A091925*A002117+225*A000796*A013663)/320.

A277117 Decimal expansion of e^6/(Pi^5+Pi^4), where e = exp(1).

Original entry on oeis.org

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

Offset: 1

Paulo Romero Zanconato Pinto, Sep 30 2016

			1.0000000438081076299476374320122890058190409215306036959233520...

D. Wilson, pers. comm.

Eric Weisstein's World of Mathematics, Almost Integer
Wikipedia, Near-identities involving e and pi.

Cf. A000796, A001113, A092425, A092731, A092512, A239606.

RealDigits[E^6/(Pi^5+Pi^4),10,120][[1]] (* Harvey P. Dale, Apr 07 2019 *)

exp(6)/(Pi^5+Pi^4) \\ Michel Marcus, Oct 02 2016

Equals A092512 /(A092731 + A092425).

A376994 Decimal expansion of Pi^4 + Pi^5.

Original entry on oeis.org

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

Offset: 3

Stefano Spezia, Oct 12 2024

This constant is very close to e^6 = A092512.

			403.4287758192838904991816427321407177300282923...

Index entries for transcendental numbers.

Cf. A092425, A092512, A092731.

Mathematica
```
RealDigits[Pi^4+Pi^5,10,100][[1]]
```

cp's OEIS Frontend

A222074 Decimal expansion of (1/1920)*Pi^5.

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A222075 Decimal expansion of (64/10395)*Pi^5.

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A309926 Decimal expansion of Pi^5/Zeta(5).

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A060302 Decimal expansion of (Pi^4 + Pi^5)^(1/6).

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A378408 Decimal expansion of Pi^5/90.

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A194656 Decimal expansion of (2*Pi^5*log(2) - 30*Pi^3*zeta(3) + 225*Pi*zeta(5))/320.

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A277117 Decimal expansion of e^6/(Pi^5+Pi^4), where e = exp(1).

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A194656 Decimal expansion of (2Pi^5log(2) - 30Pi^3zeta(3) + 225Pizeta(5))/320.