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 1-7 of 7 results.

A245294 Decimal expansion of the square root of 6/5.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

Decimal expansion of the Landau-Kolmogorov constant C(4,2) for derivatives in the case L_infinity(infinity, infinity).
See A245198.
Apart from the first digit the same as A176057. - R. J. Mathar, Jul 21 2014

Examples

			1.095445115010332226913939565601604267905489389995966508453788899464986554...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[4, 2], 10, 105] // First
RealDigits[Sqrt[6/5], 10, 100][[1]] (* Amiram Eldar, Jul 19 2022 *)
  • PARI
    sqrt(6/5) \\ Charles R Greathouse IV, Aug 26 2017

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(4,2) = sqrt(6/5).
Equals Sum_{k>=0} binomial(2*k,k)/24^k. - Amiram Eldar, Jul 19 2022

A245293 Decimal expansion of the Landau-Kolmogorov constant C(4,1) for derivatives in the case L_infinity(infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.0809601238456275151880801506365456492375770747255234380135664425927599...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[4, 1], 10, 105] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(4,1) = 4*(2/3)^(1/4)/5^(3/4) = (512/375)^(1/4).

A245295 Decimal expansion of the Landau-Kolmogorov constant C(4,3) for derivatives in the case L_infinity(infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.480165608984570501133579932327673638598123582612376236649724811831493373...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[4, 3], 10, 105] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(4,3) = (3/5)^(1/4)*2^(3/4) = (24/5)^(1/4).

A245296 Decimal expansion of the Landau-Kolmogorov constant C(5,1) for derivatives in the case L_infinity(infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.0442579093097951434453696171557025830804208042025372077576134158002325888...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,1], 10, 105] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(5,1) = (5*5^(4/5))/(8*2^(4/5)*3^(1/5)) = (1953125/1572864)^(1/5).

A245297 Decimal expansion of the Landau-Kolmogorov constant C(5,2) for derivatives in the case L_infinity(infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.1166459711038098826457154510731531789665120066974040164563421606...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,2], 10, 101] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(5,2) = (5*5^(4/5))/(8*2^(4/5)*3^(1/5)) = (1953125/1572864)^(1/5).

A245298 Decimal expansion of the Landau-Kolmogorov constant C(5,3) for derivatives in the case L_infinity(infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.11942373173510761162971108208126104124998556705860708652098279913...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,3], 10, 104] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(5,3) = (1/2)*(15/2)^(2/5).

A245299 Decimal expansion of the Landau-Kolmogorov constant C(5,4) for derivatives in the case L_infinity(-infinity, infinity).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Jul 17 2014

Keywords

Comments

See A245198.

Examples

			1.49627786973884473850810213932978255331700624709325410308756863950368...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

  • Mathematica
    a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,4], 10, 105] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(5,4) = (15/2)^(1/5).
Showing 1-7 of 7 results.

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