A131563 -id:A131563 - cp's OEIS frontend

A159820 Continued fraction for ePiphi A131563, where phi = (1 + sqrt(5))/2.

13, 1, 4, 2, 13, 3, 1, 1, 7, 3, 30, 1, 7, 1, 1, 40, 2, 6, 2, 1, 35, 4, 1, 3, 3, 1, 3, 3, 8, 1, 1, 4, 3, 5, 7, 1, 1, 1, 1, 2, 1, 2, 2, 1, 188, 3, 2, 1, 7, 1, 1, 13, 1, 7, 28, 2, 2, 47, 31, 1, 1, 1, 5, 3, 1, 7, 2, 3, 1, 3, 2, 1, 3, 4, 4, 2, 1, 1, 3, 1, 1, 1, 3, 4, 1, 19, 225, 1, 1, 16, 1, 1, 1, 1, 11, 4, 3, 1

Offset: 0

Harry J. Smith, Apr 26 2009

nonn

			e*Pi*phi = 13.8175802271764... = 13 + 1/(1 + 1/(4 + 1/(2 + 1/(13 + ...)))).

Harry J. Smith, Table of n, a(n) for n = 0..20000

ContinuedFraction[E Pi GoldenRatio,100] (* Harvey P. Dale, Aug 09 2016 *)

{ allocatemem(932245000); default(realprecision, 21000); phi = (1 + sqrt(5))/2; x=contfrac(exp(1)*Pi*phi); for (n=1, 20001, write("b159820.txt", n-1, " ", x[n])); }

A133055 Decimal expansion of e + Pi + phi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 10 2007

			7.477908470798733...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A001113, A000796, A001622, A131563.

RealDigits[E + Pi + GoldenRatio, 10, 50][[1]] (* G. C. Greubel, Oct 03 2017 *)

exp(1) + Pi + (1+sqrt(5))/2 \\ G. C. Greubel, Oct 03 2017

Terms a(29) onward added by G. C. Greubel, Oct 03 2017

A135000 Decimal expansion of egammaPi*phi, where gamma is the Euler-Mascheroni constant and phi is the golden ratio.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 21 2007

			............ e = 2.718281828459045235...
........ gamma = 0.577215664901532860...
........... Pi = 3.141592635589793238...
.......... phi = 1.618033988749894848...
e*gamma*Pi*phi = 7.975723758159953712...

Harry J. Smith, Table of n, a(n) for n = 1..20000

Cf. A001113 (e), A001620 (gamma), A000796 (Pi), A001622 (phi), A131563 (e*Pi*phi).

SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1)*EulerGamma(R)*Pi(R)*(1+Sqrt(5))/2; // G. C. Greubel, Aug 29 2018

RealDigits[E*EulerGamma*Pi*GoldenRatio, 10, 120][[1]] (* Harvey P. Dale, Sep 19 2012 *)

{ default(realprecision, 20080); phi = (1 + sqrt(5))/2; x=exp(1)*Euler*Pi*phi; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b135000.txt", n, " ", d)); } \\ Harry J. Smith, Apr 26 2009

More terms from Harry J. Smith, Apr 26 2009

A133065 Decimal expansion of (ePiPhi)^(1/2).

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 09 2007

phi = (1 + sqrt(5))/2 = 1.61803...

			3.7172005901...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A131563, A131566.

RealDigits[Sqrt[E*Pi*GoldenRatio], 10, 50][[1]] (* G. C. Greubel, Oct 20 2017 *)

sqrt(exp(1)*Pi*(1+sqrt(5))/2) \\ G. C. Greubel, Oct 20 2017

A135155 Decimal expansion of ePiphi/5.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 26 2007

Phi is the golden ratio.

			2.763516045435...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A131563.

RealDigits[(E Pi GoldenRatio)/5, 10, 2000][[1]] (* G. C. Greubel, Sep 29 2016 *)

A133056 Decimal expansion of (e + Pi + phi)/2.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 10 2007

			3.738954235399366661...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A001113, A000796, A001622, A131563.

RealDigits[(E + Pi + GoldenRatio)/2, 10, 50][[1]] (* G. C. Greubel, Oct 03 2017 *)

(exp(1) + Pi + (1+sqrt(5))/2)/2 \\ G. C. Greubel, Oct 03 2017

Terms a(29) onward added by G. C. Greubel, Oct 03 2017

A133057 Decimal expansion of (e + Pi + phi)/3.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 10 2007

			2.492636156932911...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A001113, A000796, A001622, A131563.

RealDigits[(E + Pi + GoldenRatio)/3, 10, 50][[1]] (* G. C. Greubel, Oct 03 2017 *)

(exp(1) + Pi + (1+sqrt(5))/2)/3 \\ G. C. Greubel, Oct 03 2017

Terms a(29) onward added by G. C. Greubel, Oct 03 2017

A133066 Decimal expansion of (ePiPhi)^(1/3).

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 09 2007

phi = (1 + sqrt(5))/2 = 1.61803...

			2.39962842784...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A131563, A131566, A133065.

RealDigits[N[(E \[Pi] GoldenRatio)^(1/3),80]][[1]]  (* Harvey P. Dale, Feb 08 2011 *)

(exp(1)*Pi*(1+sqrt(5))/2)^(1/3) \\ G. C. Greubel, Oct 20 2017

More terms from Harvey P. Dale, Feb 08 2011

A135154 Decimal expansion of ePiphi/2.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 26 2007

Phi is the golden ratio.

			6.908790113588247...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A131563.

RealDigits[(E Pi GoldenRatio)/2,10,120][[1]] (* Harvey P. Dale, Aug 27 2013 *)

More terms from Harvey P. Dale, Aug 27 2013

A135183 Decimal expansion of ePiphi/3, where phi is the golden ratio.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 26 2007

			4.605860075725498...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A131563.

RealDigits[(E Pi GoldenRatio)/3,10,120][[1]] (* Harvey P. Dale, Aug 08 2013 *)

exp(1)*Pi*(1+sqrt(5))/6 \\ Charles R Greathouse IV, Sep 30 2016

More terms from Harvey P. Dale, Aug 08 2013

cp's OEIS Frontend

A159820 Continued fraction for e*Pi*phi A131563, where phi = (1 + sqrt(5))/2.

Views

Author

Keywords

Examples

Links

Programs

Mathematica

PARI

A133055 Decimal expansion of e + Pi + phi.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A135000 Decimal expansion of e*gamma*Pi*phi, where gamma is the Euler-Mascheroni constant and phi is the golden ratio.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A133065 Decimal expansion of (e*Pi*Phi)^(1/2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A135155 Decimal expansion of e*Pi*phi/5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A133056 Decimal expansion of (e + Pi + phi)/2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A133057 Decimal expansion of (e + Pi + phi)/3.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A133066 Decimal expansion of (e*Pi*Phi)^(1/3).

Views

Author

Keywords

A159820 Continued fraction for ePiphi A131563, where phi = (1 + sqrt(5))/2.

A135000 Decimal expansion of egammaPi*phi, where gamma is the Euler-Mascheroni constant and phi is the golden ratio.

A133065 Decimal expansion of (ePiPhi)^(1/2).

A135155 Decimal expansion of ePiphi/5.

A133066 Decimal expansion of (ePiPhi)^(1/3).

A135154 Decimal expansion of ePiphi/2.

A135183 Decimal expansion of ePiphi/3, where phi is the golden ratio.