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.

User: Volker Werner

Volker Werner's wiki page.

Volker Werner has authored 21 sequences. Here are the ten most recent ones:

A182552 Decimal expansion of phi^(1/e), where phi is the golden ratio.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			1.19366444040858744551219931400262182977345282047683...

Crossrefs

Cf. A000796, A001622, A139341

Programs

  • Mathematica
    RealDigits[ N[GoldenRatio^(1/E), 105]] [[1]]

Formula

Equals A001622^(1/A001113).

A182551 Decimal expansion of gamma^(1/e), where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			0.81696075941989309813765514103027697644211120879263...

Links

Crossrefs

Cf. A001113, A001620, A073004, A094644.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)^(1/Exp(1)); // G. C. Greubel, Sep 06 2018
  • Mathematica
    RealDigits[ N[EulerGamma^(1/E), 105]][[1]]
  • PARI
    default(realprecision, 100); Euler^(1/exp(1)) \\ G. C. Greubel, Sep 06 2018

Formula

Equals A001620^(1/A001113).

A182550 Decimal expansion of Pi^(1/phi), where phi is the golden ratio.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			2.02887606546321308403656793466426896286048157296775...

Crossrefs

Cf. A000796, A001622.

Programs

  • Mathematica
    RealDigits[ N[Pi^(1/GoldenRatio), 105]] [[1]]

Formula

Equals A000796^(1/A001622).

A182549 Decimal expansion of Pi^phi, where phi is the golden ratio.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			6.37390214230339465167164790877525198315514462131682...

Crossrefs

Cf. A000796, A001622.

Programs

  • Mathematica
    RealDigits[ N[Pi^GoldenRatio, 105]] [[1]]

Formula

Equals A000796^A001622.

Extensions

a(105) corrected by Georg Fischer, Jul 16 2021

A182548 Decimal expansion of Pi^(1/gamma), where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			7.26590375436605603996051715583327875706572154615430...

Links

Crossrefs

Cf. A000796, A001620.

Programs

  • Magma
    R:= RealField(100);  Pi(R)^(1/EulerGamma(R)); // G. C. Greubel, Sep 06 2018
  • Mathematica
    RealDigits[ N[Pi^(1/EulerGamma), 105]][[1]]
  • PARI
    default(realprecision, 100); Pi^(1/Euler) \\ G. C. Greubel, Sep 06 2018

Formula

Equals A000796^(1/A001620).

A182547 Decimal expansion of Pi^gamma, where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			1.93625563341967446001393463894632996029116201430656...

Links

Crossrefs

Cf. A000796, A001620, A182470.

Programs

  • Magma
    R:= RealField(100); Pi(R)^EulerGamma(R); // G. C. Greubel, Sep 03 2018
  • Mathematica
    RealDigits[ N[Pi^EulerGamma, 105]] [[1]]
  • PARI
    default(realprecision, 100); Pi^Euler \\ G. C. Greubel, Sep 03 2018

Formula

Equals A000796^A001620.

A182546 Decimal expansion of | log_phi(i) |, where phi is the golden ratio and i is the imaginary unit.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Examples

			3.26425130263649690673153367843629490781491039315880...

Crossrefs

Cf. A000796, A001622, A202543.

Programs

  • Mathematica
    RealDigits[ Im[N[Log[I]/Log[GoldenRatio], 105]]] [[1]]
RealDigits[Abs[Log[GoldenRatio,I]],10,120][[1]] (* Harvey P. Dale, Sep 22 2018 *)

Formula

Equals |Im(Log(i))/Log(A001622)|
Equals Pi/log(phi+1) = A000796/A202543. - Gleb Koloskov, Sep 28 2021

A182545 Decimal expansion of | log_phi(gamma) |, where phi is the golden ratio and gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Comments

Reciprocal of A182527.

Examples

			1.14199045901163848991246208812017742957155235615017...

Links

Crossrefs

Cf. A001620, A001622, A182527.

Programs

  • Magma
    SetDefaultRealField(RealField(100)); R:= RealField(); phi:=(1+Sqrt(5))/2; -Log(EulerGamma(R))/Log(phi); // G. C. Greubel, Sep 01 2018
  • Mathematica
    RealDigits[ N[Log[EulerGamma]/Log[GoldenRatio], 105]] [[1]]
  • PARI
    default(realprecision, 100); phi=(1+sqrt(5))/2; -log(Euler)/log(phi) \\ G. C. Greubel, Sep 01 2018

Formula

Equals 1/A182527.

A182516 Decimal expansion of log_phi(Pi), where phi is the golden ratio.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 04 2012

Keywords

Comments

Reciprocal of A182501.

Examples

			2.37884820413050452387240639107665194916013848483363...

Crossrefs

Cf. A000796, A001622, A182501.

Programs

  • Mathematica
    RealDigits[ N[Log[Pi]/Log[GoldenRatio], 105]] [[1]]

Formula

Equals 1/A182501.

A182528 Decimal expansion of | log_gamma(i) |, where gamma is the Euler-Mascheroni constant and i is the imaginary unit.

Original entry on oeis.org

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

Views

Author

Volker Werner, May 03 2012

Keywords

Examples

			2.85838754332642773168967584118090542016409347654787...

Crossrefs

Cf. A001622.

Programs

  • Mathematica
    RealDigits[ Im[ N[Log[I]/Log[EulerGamma], 105]]] [[1]]

Formula

Equals |Im(Log(i))/Log(A001622)|

Extensions

a(105) corrected by Sean A. Irvine, Jul 20 2021

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