cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A053004 Decimal expansion of AGM(1,sqrt(2)).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Feb 21 2000

Keywords

Comments

AGM(a,b) is the limit of the arithmetic-geometric mean iteration applied repeatedly starting with a and b: a_0=a, b_0=b, a_{n+1}=(a_n+b_n)/2, b_{n+1}=sqrt(a_n*b_n).

Examples

			1.19814023473559220743992249228...

References

  • George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 195.
  • J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, page 5.
  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.1, p. 420.
  • J. R. Goldman, The Queen of Mathematics, 1998, p. 92.

Links

Crossrefs

Cf. A014549, A053002, A053003, A076390, A085565, A096427.

Programs

  • Maple
    evalf(GaussAGM(1, sqrt(2)), 144);  # Alois P. Heinz, Jul 05 2023
  • Mathematica
    RealDigits[ N[ ArithmeticGeometricMean[1, Sqrt[2]], 105]][[1]] (* Jean-François Alcover, Jan 30 2012 *)
RealDigits[N[(1+Sqrt[2])Pi/(4EllipticK[17-12Sqrt[2]]), 105]][[1]] (* Jean-François Alcover, Jun 02 2019 *)
  • PARI
    default(realprecision, 20080); x=agm(1, sqrt(2)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b053004.txt", n, " ", d)) \\ Harry J. Smith, Apr 20 2009
  • PARI
    2*real(agm(1, I)/(1+I)) \\ Michel Marcus, Jul 26 2018
  • Python
    from mpmath import mp, agm, sqrt
mp.dps=106
print([int(z) for z in list(str(agm(1, sqrt(2))).replace('.', '')[:-1])]) # Indranil Ghosh, Jul 11 2017

Formula

Equals Pi/(2*A085565). - Nathaniel Johnston, May 26 2011
Equals Integral_{x=0..Pi/2} sqrt(sin(x)) or Integral_{x=0..1} sqrt(x/(1-x^2)). - Jean-François Alcover, Apr 29 2013 [cf. Boros & Moll p. 195]
Equals Product_{n>=1} (1+1/A033566(n)) and also 2*AGM(1, i)/(1+i) where i is the imaginary unit. - Dimitris Valianatos, Oct 03 2016
Conjecturally equals 1/( Sum_{n = -infinity..infinity} exp(-Pi*(n+1/2)^2 ) )^2. Cf. A096427. - Peter Bala, Jun 10 2019
From Amiram Eldar, Aug 26 2020: (Start)
Equals 2 * A076390.
Equals Integral_{x=0..Pi} sin(x)^2/sqrt(1 + sin(x)^2) dx. (End)
Equals sqrt(2/Pi)*Gamma(3/4)^2 = Integral_{x = 0..1} 1/(1 - x^2)^(1/4) dx = Pi/Integral_{x = 0..1} 1/(1 - x^2)^(3/4) dx. - Peter Bala, Jan 05 2022
From Peter Bala, Mar 02 2022: (Start)
Equals 2*Integral_{x = 0..1} x^2/sqrt(1 - x^4) dx.
Equals 1 - Integral_{x = 0..1} (sqrt(1 - x^4) - 1)/x^2 dx.
Equals hypergeom([-1/2, -1/4], [3/4], 1) = 1 + Sum_{n >= 0} 1/(4*n + 3)*Catalan(n)*(1/2^(2*n+1)). Cf. A096427. (End)

Extensions

More terms from James Sellers, Feb 22 2000

A175573 Decimal expansion of Pi^(1/4)/Gamma(3/4).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Jul 15 2010

Keywords

Comments

Entry 34 a of chapter 11 of Ramanujan's second notebook. Entry 34 b is A085565.

Examples

			1.0864348112133080145753161...

Links

Crossrefs

Cf. A068465, A085565, A092040, A096427, A175574, A247217, A273081, A273082, A273083, A273084, A319332, A327995.

Programs

  • Magma
    C := ComplexField(); [(Pi(C))^(1/4)/Gamma(3/4)]; // G. C. Greubel, Nov 05 2017
  • Maple
    Pi^(1/4)/GAMMA(3/4) ; evalf(%) ;
  • Mathematica
    RealDigits[ Pi^(1/4)/Gamma[3/4], 10, 105][[1]] (* Jean-François Alcover, Jul 04 2013 *)
  • PARI
    Pi^(1/4)/gamma(3/4) \\ G. C. Greubel, Nov 05 2017
  • PARI
    2*suminf(k=0,exp(-Pi)^(k^2))-1 \\ Hugo Pfoertner, Sep 17 2018

Formula

Equals A092040 / A068465.
Equals Sum_{n=-oo..oo} exp(-Pi*n^2), or also EllipticTheta(3, 0, exp(-Pi)). - Jean-François Alcover, Jul 04 2013
Equals sqrt(A175574). - Amiram Eldar, Jul 04 2023
Equals Gamma(1/4)/(sqrt(2)*Pi^(3/4)). - Vaclav Kotesovec, Jul 04 2023
Equals Product_{k>=1} tanh((1/2 + i/2)*Pi*k), i=sqrt(-1). - _Antonio Graciá Llorente, Mar 20 2024
Equals Product_{k>=0} (1/2)*(((k+1/2)/(k+1))^(1/2)+((k+1)/(k+1/2))^(1/2)). - Antonio Graciá Llorente, Jul 23 2024
Equals (1/A096427)^2 (see Spanier and Oldham at p. 258). - Stefano Spezia, Dec 31 2024
Equals 2*A319332 = 1/A327995. - Hugo Pfoertner, Dec 31 2024

A224268 Decimal expansion of Product_{n>=1} (1 - 1/(4n+1)^2).

Original entry on oeis.org

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

Views

Author

Bruno Berselli, Apr 02 2013

Keywords

Examples

			0.9270373386506859592169251735976300231087994117608834527929640225280...

References

  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.

Links

Crossrefs

Cf. A064853, A085565, A093341, A327996.
Cf. product(1-1/(4n+r)^2, n>=1): A096427 (r=-1), A112628 (r=0), A179587-1 (r=2).

Programs

  • Mathematica
    RealDigits[N[Product[1 - 1/(4 n + 1)^2, {n, 1, Infinity}], 90]][[1]] (* or, by the formula: *) RealDigits[Gamma[1/4]^2/(8 Sqrt[Pi]), 10, 90][[1]]
  • PARI
    prodnumrat(1 - 1/(4*n+1)^2, 1) \\ Charles R Greathouse IV, Feb 07 2025

Formula

Equals Gamma(1/4)^2/(8*sqrt(Pi)) = L/(4*sqrt(2)), where L is the Lemniscate constant (A064853).
From Peter Bala, Feb 26 2019: (Start)
C = (Pi/4)*( Sum_{n = -inf..inf} exp(-Pi*n^2) )^2.
C = (-1)^m*2^(2*m+1)/Catalan(m) * Product_{n >= 1} ( 1 - (4*m + 3)^2/(4*n + 1)^2 ), for m = 0,1,2,....
C = Integral_{x = 0..1} 1/sqrt(1 + x^4) dx.
C = (1/sqrt(2))*Integral_{x = 0..1} 1/sqrt(1 - x^4) dx.
C = (3/2)*Integral_{x = 0..1} sqrt(1 + x^4) dx - sqrt(2)/2.
C = (1/8)*Integral_{x = 0..1} 1/(x - x^2)^(3/4) dx.
C = Sum_{n >= 0} binomial(-1/2,n)/(4*n + 1) = Sum_{n >= 0} binomial(2*n,n)/4^n * 1/(4*n + 1).
C = (1/2)*Sum_{n >= 0} (-1)^n*binomial(-3/4,n)/(4*n + 1).
Continued fraction: 1 - 1/(5 + 20/(1 + 30/(3 + ... + (4*n)*(4*n + 1)/(1 + (4*n + 1)*(4*n + 2)/(3 + ... ))))).
C = A085565/sqrt(2). C = Pi/(4*A096427). (End)
Equals A093341/2 = A327996^2. - Hugo Pfoertner, Oct 31 2024

A175574 Decimal expansion of sqrt(Pi) / (Gamma(3/4))^2.

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Jul 15 2010

Keywords

Comments

Entry 34 c of chapter 11 of Ramanujan's second notebook.
This constant is also the ratio T(Pi/2)/T(0), where T(Pi/2) is the exact pendulum period for an amplitude of Pi/2 and T(0) the approximate period 2*Pi*sqrt(L/g) for small angles. - Jean-François Alcover, Aug 05 2014

Examples

			1.18034059901609622604533794..

Links

Crossrefs

Cf. A002161, A068465, A085565, A096427, A175573.

Programs

  • MATLAB
    sqrt(pi)/gamma(3/4)^2 % Altug Alkan, Dec 05 2015
  • Maple
    sqrt(Pi)/GAMMA(3/4)^2 ; evalf(%) ;
  • Mathematica
    First@ RealDigits[N[Sqrt@ Pi/Gamma[3/4]^2, 120]] (* Michael De Vlieger, Dec 06 2015 *)
  • PARI
    sqrt(Pi)/gamma(3/4)^2 \\ Altug Alkan, Dec 05 2015

Formula

Equals A002161 /A068465^2.
Equals 2F1([1/2,1/2],[1],1/2) = 1/agm(1, sqrt(1/2)) = gamma(1/4)^2/(2*Pi^(3/2)).
Equals 2*sqrt(2)*K(-1)/Pi, where K is the complete elliptic integral of the first kind, K(-1) being A085565. - Jean-François Alcover, Jun 03 2014
Equals Product_{k>=1} (1-(-1)^k/(2*k)) = 3/2 * 3/4 * 7/6 * 7/8 * 11/10 * 11/12 * ... . - Richard R. Forberg, Dec 05 2015
Reciprocal of A096427. Equals ( Sum_{n = -inf..inf} exp(-Pi*n^2) )^2, a rapidly converging series. For example, summing from n = -5 to n = 5 gives the constant correct to 49 decimal places. - Peter Bala, Mar 06 2019
Equals Sum_{k>=0} binomial(2*k,k)^2/2^(5*k). - Amiram Eldar, Aug 26 2020
Equals (3/2)*hypergeom([-1/4, 3/4], [3/2], 1). - Peter Bala, Mar 04 2022
Equals A175573^2. - Amiram Eldar, Jul 04 2023

Extensions

A-number typo for sqrt(Pi) corrected by R. J. Mathar, Aug 01 2010

A254794 Decimal expansion of L^2/Pi where L is the lemniscate constant A062539.

Original entry on oeis.org

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

Views

Author

Peter Bala, Feb 22 2015

Keywords

Comments

Brouncker gave the generalized continued fraction expansion 4/Pi = 1 + 1^2/(2 + 3^2/(2 + 5^2/(2 + ... ))). More generally, Osler shows that the continued fraction n + 1^2/(2*n + 3^2/(2*n + 5^2/(2*n + ... ))) equals a rational multiple of 4/Pi or its reciprocal when n is a positive odd integer, and equals a rational multiple of L^2/Pi or its reciprocal when n is a positive even integer.

Examples

			2.18843961522647663883676994070446454325937272282556672211928621....

References

  • O. Perron, Die Lehre von den Kettenbrüchen, Band II, Teubner, Stuttgart, 1957

Links

Crossrefs

Cf. A000796, A062539, A254795, A254796, A096427, A133748, A224268.

Programs

  • Magma
    SetDefaultRealField(RealField(110)); 2*(Gamma(5/4)/Gamma(3/2))^4; // G. C. Greubel, Mar 06 2019
  • Maple
    #A254794
digits:=105:
2*( GAMMA(5/4)/GAMMA(3/2) )^4:
evalf(%);
  • Mathematica
    RealDigits[2*(Gamma[5/4]/Gamma[3/2])^4, 10, 110][[1]] (* G. C. Greubel, Mar 06 2019 *)
  • PARI
    default(realprecision, 110); 2*(gamma(5/4)/gamma(3/2))^4 \\ G. C. Greubel, Mar 06 2019
  • Sage
    numerical_approx(2*(gamma(5/4)/gamma(3/2))^4, digits=110) # G. C. Greubel, Mar 06 2019

Formula

L^2/Pi = 2*( (1/4)!/(1/2)! )^4 = 9/4*( (1/4)!/(3/4)! )^2.
L^2/Pi = lim_{n -> oo} (4*n + 2) * Product {k = 0..n} ( (4*k - 1)/(4*k + 1) )^2
Generalized continued fraction: L^2/Pi = 2 + 1^2/(4 + 3^2/(4 + 5^2/(4 + ... ))). This is the particular case n = 0, x = 2 of a result of Ramanujan - see Berndt et al., Entry 25. See also Perron, p. 35.
The sequence of convergents to Ramanujan's continued fraction begins [2/1, 9/4, 54/25, 441/200, 4410/2025, ...]. See A254795 for the numerators and A254796 for the denominators.
Another continued fraction is L^2/Pi = 1 + 2/(1 + 1*3/(2 + 3*5/(2 + 5*7/(2 + 7*9/(2 + ... ))))), which can be transformed into the slowly converging series: L^2/Pi = 1 + 4 * Sum {n >= 0} P(n)^2/(4*n + 5), where P(n) = Product {k = 1..n} (4*k - 1)/(4*k + 1).
(L^2/Pi)^2 = 3 + 2*( 1^2/(1 + 1^2/(3 + 3^2/(1 + 3^2/(3 + 5^2/(1 + 5^2/(3 + ... )))))) ) follows by setting n = 0, x = 2 in Entry 26 of Berndt et al.
From Peter Bala, Feb 28 2019: (Start)
C = 2*A224268/A096427.
For m = 0,1,2,..., C = 4*(m + 1)*P(m)/Q(m), where P(m) = Product_{n >= 1} ( 1 - (4*m + 3)^2/(4*n + 1)^2 ) and Q(m) = Product_{n >= 0} ( 1 - (4*m + 1)^2/(4*n + 3)^2 ).
For m = 0,1,2,..., C = - Product_{k = 1..m} (1 - 4*k)/(1 + 4*k) * Product_{n >= 0} ( 1 - (4*m + 2)^2/(4*n + 1)^2 ) and
1/C = Product_{k = 0..m} (1 + 4*k)/(1 - 4*k) * Product_{n >= 0} ( 1 - (4*m + 2)^2/(4*n + 3)^2 ).
C = (Pi/2) * ( Sum_{n = -oo..oo} exp(-Pi*n^2) )^4. (End)
Equals A133748/Pi. - Hugo Pfoertner, Apr 13 2024

A309893 Decimal expansion of AGM(1, sqrt(3)/2).

Original entry on oeis.org

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

Views

Author

Daniel Hoyt, Aug 21 2019

Keywords

Comments

Related to the pendulum acceleration relation at 60 degrees. In general, the period T of a mathematical pendulum with a maximum deflection angle theta is 2*Pi*sqrt(L/g)/AGM(1, cos(theta/2)), where L is the length of the pendulum, g is the gravitational acceleration, and 0 < theta <= 90 degrees. For theta = 60 degrees, the period is T = 2*Pi*sqrt(L/g)/AGM(1, sqrt(3)/2). - Jianing Song, Nov 21 2022

Examples

			0.931808391622448271177844...

Links

Crossrefs

Cf. A310000 (AGM(1, cos(Pi/5))), A096427 (AGM(1, sqrt(2)/2)), A053004, A014549, A068521.

Programs

  • Mathematica
    RealDigits[ArithmeticGeometricMean[1, Sqrt[3]/2], 10, 100][[1]] (* Amiram Eldar, Aug 21 2019 *)
  • PARI
    agm(1, sqrt(3)/2) \\ Michel Marcus, Aug 22 2019
  • Python
    import decimal
prec = int(input('Precision: '))
decimal.getcontext().prec = prec
D = decimal.Decimal
def agm(a, b):
    for x in range(prec):
        a, b = (a + b) / 2,(a * b).sqrt()
    return a
print(agm(1, D(3).sqrt()/2))
  • Sage
    RealField(300)(1.0).agm(sqrt(3)/2) # Peter Luschny, Aug 22 2019

Formula

AGM(1, sin(Pi/3)).

A159570 Continued fraction for 1/(sqrt(2)*G), where G is Gauss's constant A014549.

Original entry on oeis.org

0, 1, 5, 1, 1, 5, 20, 1, 13, 2, 1, 1, 61, 1, 1, 2, 4, 1, 3, 1, 2, 1, 5, 1, 13, 1, 11, 7, 6, 2, 77, 7, 1, 5, 4, 8, 1, 1, 6, 4, 2, 1, 1, 2, 4, 1, 1, 2, 1, 3, 1, 1, 6, 6, 1, 7, 1, 10, 1, 1, 4, 1, 4, 2, 1, 7, 1, 4, 1, 2, 17, 2, 2, 1, 5, 2, 1, 2, 1, 1, 1, 3, 3, 1, 1, 6, 1, 1, 16, 3, 1320, 2, 2, 7, 5, 9, 1, 217, 3
Offset: 0

Views

Author

Harry J. Smith, Apr 16 2009

Keywords

Comments

Continued fraction for A096427.
Also called the Ubiquitous Constant.

Examples

			0.847213084793979086606499123... = 0 + 1/(1 + 1/(5 + 1/(1 + 1/(1 + ...))))

Links

Crossrefs

Cf. A096427.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(2*Pi(R)^(3/2)/Gamma(1/4)^2); // G. C. Greubel, Sep 28 2018
  • Mathematica
    ContinuedFraction[2*Pi^(3/2)/Gamma[1/4]^2, 100] (* G. C. Greubel, Sep 28 2018 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, sqrt(1/2))); for (n=0, 20000, write("b159570.txt", n, " ", x[n+1])); }
  • PARI
    default(realprecision, 100); contfrac(2*Pi^(3/2)/gamma(1/4)^2) \\ G. C. Greubel, Sep 28 2018

A371466 Decimal expansion of Product_{k>=1} (1 - 1/(3*k+1)^2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Mar 31 2024

Keywords

Examples

			0.8833193751427249786568447498242193512859342691...

Crossrefs

Cf. A003881, A010503, A086089, A096427, A224268, A290570, A371467.

Programs

  • Mathematica
    RealDigits[Gamma[1/3]^3/(4 Sqrt[3] Pi), 10, 100][[1]]

Formula

Equals Gamma(1/3)^3 / (4 * sqrt(3) * Pi).
Equals A290570/2. - Hugo Pfoertner, Mar 31 2024
Equals Integral_{x=0..1} (1-x^3)^(1/3) dx. - Mikhail Kurkov, Jun 29 2025

A371467 Decimal expansion of Product_{k>=0} (1 - 1/(3*k+2)^2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Mar 31 2024

Keywords

Examples

			0.6844634059797257270110769788663463289556838...

Crossrefs

Cf. A003881, A010503, A086089, A096427, A224268, A224273, A371466.

Programs

  • Mathematica
    RealDigits[(4/3) Pi^2/Gamma[1/3]^3, 10, 100][[1]]

Formula

Equals (4/3) * Pi^2 / Gamma(1/3)^3.
Equals 1/A224273. - Hugo Pfoertner, Mar 31 2024
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