A091925 -id:A091925 - cp's OEIS frontend

A382867 Decimal expansion of (Pi^3)/31.

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

Offset: 1

Jason Bard, Jun 12 2025

			1.0002024735580587153379456473258514581362996311575...

Jason Bard, Table of n, a(n) for n = 1..10000
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.
Index entries for transcendental numbers

Cf. A091925, A000796.

Mathematica
```
RealDigits[Pi^3/31, 10, 100][[1]]
```

A096439 Decimal expansion of (Pi^3 - e^3)^(1/2).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, Aug 10 2004

			3.304654256819032564155324312900...

Cf. A091925, A091933, A096388.

RealDigits[Sqrt[Pi^3-E^3],10,120][[1]] (* Harvey P. Dale, May 05 2022 *)

A096440 Decimal expansion of (Pi^3 - e^3)^(1/3).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, Aug 10 2004

			2.218625597156644840987057437898...

Cf. A091925, A091933, A096388.

(Pi^3 - exp(3))^(1/3) \\ Michel Marcus, Mar 11 2018

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.

A225016 Decimal expansion of Pi^3/8.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 24 2013

			3.875784585037477521934539383387674400278161070735638461768067262975799364683...

Index entries for transcendental numbers

Cf. A000796, A002388, A019669, A091476, A091925.

Mathematica
```
RealDigits[Pi^3/8, 10, 100][[1]]
```

Pi^3/8 \\ Charles R Greathouse IV, Oct 01 2022

Equals Integral_{x>0} log(x)^2/(1+x^2) dx.
Equals Integral_{x=0..Pi/2} log(tan(x))^2 dx.
Equals Integral_{x=0..Pi/2} log(sin(x)^3)*log(sin(x))-(3*Pi/2)*log(2)^2 dx.
Equals (27/7) * Sum_{k>=0} binomial(2*k, k)/((2*k+1)^3*16^k);
Equals (27/7) * 4F3([1/2, 1/2, 1/2, 1/2], [3/2, 3/2, 3/2], 1/4), where pFq() is the generalized hypergeometric function.
From Amiram Eldar, Aug 21 2020: (Start)
Equals Integral_{x=0..oo} x^2/cosh(x) dx.
Equals 2 + Integral_{x=0..oo} x^2 * exp(-x) * tanh(x) dx. (End)
From Gleb Koloskov, Jun 15 2021: (Start)
Equals 2*Integral_{x=0..1} log(x)^2/(1+x^2) dx.
Equals 2*Integral_{x=1..oo} log(x)^2/(1+x^2) dx.
Equals 2*(-1)^n*Integral_{x=-1/e..0} W(n,x)*(1-W(n,x))*log(-W(n,x))^2/x/(1-W(n,x)^4) dx, where W=LambertW, for n=0 and n=-1. (End)

Offset corrected by Rick L. Shepherd, Jan 01 2014

A245719 Decimal expansion of the skewness of the Gumbel distribution.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Jul 30 2014

			1.139547099404648657492793019389846112087599795836551824721655710085248...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365.

Eric Weisstein's MathWorld, Gumbel Distribution.
Wikipedia, Gumbel Distribution.

Cf. A002117, A010464, A091925.

RealDigits[12*Sqrt[6]*Zeta[3]/Pi^3, 10, 100] // First

12*sqrt(6)*zeta(3)/Pi^3 \\ Stefano Spezia, Dec 15 2024

Equals 12*sqrt(6)*zeta(3)/Pi^3.

A325629 Floor of number of n-dimensional degrees in an n-sphere.

Original entry on oeis.org

2, 360, 41252, 3712766, 283634468, 19145326633, 1170076174384, 65816784809141, 3447793362911604, 16969079580805447, 7901760333122072321, 350023289756266797348, 14816864219294689084225

Offset: 0

Eliora Ben-Gurion, Sep 07 2019

nonn

Only the 0th and 1st terms of this sequence are exact values of n-degrees in an n-sphere, by definition. The 0-sphere, being 2 disconnected points at the ends of a segment, is trivial.
The number of degrees, minutes, seconds in an n-sphere is designed to approximate the size of an n-cube, m^n units in size, as m becomes increasingly small, observed from the center of the sphere. This makes a degree Pi/180 of a radian, a square degree (Pi/180)^2 of a steradian, a cubic degree (Pi/180)^3 of a 3-radian, etc.
The sequence has a maximum value at n = 20626 with a value of 1.3610489172...*10^4479, too large to be written here. I conjecture that the peak value of the function analytically is somewhere near 64800/Pi = 20626.48062...
At n = 56058 the sequence has a value of 281 (actual number 281.4089), meaning the 56058-dimensional sphere has less than 360 degrees. At n = 56070, the function has a value of 0.6978855, turning the rest of the sequence into a string of zeros.
An "N-sphere" is located in an N+1-dimensional space, 1-sphere being a circle, 2-sphere being an ordinary sphere, and so on.
From Jon E. Schoenfield, Sep 07 2019: (Start)
The maximum value of the continuous function is 1.361052727810610001492173640278424460497...*10^4479 and it occurs at 20626.48061662940750570152124725484602696... which is close to 64800/Pi, but it's actually 64799.99997461521504462375443773494034381.../Pi. That numerator appears to be 64800 - z/64800 + (27/10) * z^2 / 64800^3 - ... where z = zeta(2) = Pi^2 / 6. (End)

			Number of cubic degrees in a 3-sphere:
Surface area of a 3-sphere: 2*Pi^((3+1)/2) / ((3+1)/2 - 1)! = 2*Pi^2 / (2-1)! = 2*Pi^2.
Cubic degrees: 2*Pi^2 * (180/Pi)^3 = 11664000 / Pi = 3712766.512...
Number of tesseractic degrees in a 4-sphere:
Surface area of a 4-sphere: 2*Pi^((4+1)/2) / Gamma(5/2) = 2*Pi^(5/2) / (3*Pi^(1/2)/4) = 8*Pi^2/3.
Tesseractic degrees: 8*Pi^2/3 * (180/Pi)^4 = 2799360000 / Pi^2 = 283634468.641...

Eric Weisstein's World of Mathematics, Solid Angle.
Wikipedia, N-sphere
Wikipedia, Particular values of the gamma function

Surface area of k-dimensional sphere for k=2..8: A019692, A019694, A164102, A164104, A091925, A164107, A164109.

Cf. A125560.

a(n) = floor((2*Pi^((n+1)/2)/((n+1)/2-1)!)/(Pi/180)^n).
a(n) = floor((2*Pi^((n+1)/2)/(Gamma((n+1)/2)))/(Pi/180)^n).
a(n) = floor(2^(2n+1)*45^n*Pi^((n+1)/2-n)/((n+1)/2-1)!).
a(n) = floor(2^(2n+1)*45^n*Pi^((n+1)/2-n)/(Gamma((n+1)/2))).

A379334 Decimal expansion of the minimum value of the function s(t) = (Pi + 2*sqrt(1 + t^2))/(1 + Pi/2 + t) for t > 0.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Dec 21 2024

			1.65743478264911072351577202923336908988785497834...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 7.4, p. 466.

Cf. A000796, A002388, A019694, A091925.

RealDigits[2(Pi+Pi^2+Sqrt[8+Pi^3+4Pi(3+Sqrt[2+Pi])+Pi^2(7+2Sqrt[2+Pi])])/(4+Pi^2+Pi(4+Sqrt[2+Pi])),10,100][[1]]

Equals 2*(Pi + Pi^2 + sqrt(8 + Pi^3 + 4Pi*(3 + sqrt(2 + Pi)) + Pi^2*(7 + 2*sqrt(2 + Pi))))/(4 + Pi^2 + Pi*(4 + sqrt(2 + Pi))).

cp's OEIS Frontend

A382867 Decimal expansion of (Pi^3)/31.

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A096439 Decimal expansion of (Pi^3 - e^3)^(1/2).

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A096440 Decimal expansion of (Pi^3 - e^3)^(1/3).

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PARI

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

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A225016 Decimal expansion of Pi^3/8.

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Extensions

A245719 Decimal expansion of the skewness of the Gumbel distribution.

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Mathematica

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A325629 Floor of number of n-dimensional degrees in an n-sphere.

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A379334 Decimal expansion of the minimum value of the function s(t) = (Pi + 2*sqrt(1 + t^2))/(1 + Pi/2 + t) for t > 0.

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