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 1-10 of 28 results. Next

A092033 Duplicate of A061360.

Original entry on oeis.org

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

Views

Author

Keywords

A061382 Decimal expansion of Pi/e.

Original entry on oeis.org

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

Views

Author

Jason Earls, Jun 08 2001

Keywords

Examples

			Pi/e ~= 1.15572734979092171791009318331269629912...

References

  • Paul J. Nahin, "An Imaginary Tale, The Story of [Sqrt(-1)]," Princeton University Press, Princeton, NJ 1998, p. 188.

Links

Crossrefs

Cf. A061666 (continued fraction for Pi/e).
Cf. A001113, A000796, A061360.

Programs

  • Mathematica
    RealDigits[ Pi/E, 10, 110][[1]] (* Robert G. Wilson v, Jan 15 2004 *)
  • PARI
    { default(realprecision, 20080); x=Pi/exp(1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b061382.txt", n, " ", d)) } \\ Harry J. Smith, Jul 22 2009

Formula

Equals A000796 / A001113.
Equals Integral_{-oo..oo} cos(x)/(1 + x^2) dx. - Robert G. Wilson v, Jan 15 2004
Equals Integral_{-oo..oo} cos(x)/(1 + x^2)^2 dx. - Amiram Eldar, Jul 21 2020
From Robert FERREOL, Apr 02 2022: (Start)
Equals Integral_{-oo..oo} x*sin(x)/(1 + x^2) dx.
Equals 2*Integral_{-oo..oo} x*sin(x)/(1 + x^2)^2 dx. (End)
Equals Product_{k>=1} ((2*k + 1)/(2*k - 1))^(2*k)*(k/(k + 1))^(2*k + 1). - Antonio Graciá Llorente, Mar 30 2024
Equals 1/A061360. - Alois P. Heinz, Jul 14 2024
Equals Integral_{x=0..1} sin(Pi*x)/(x^x*(1 - x)^(1 - x)) dx. (See Zander link). - Peter Luschny, Oct 31 2024

A073244 Decimal expansion of Pi - e.

Original entry on oeis.org

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

Views

Author

Rick L. Shepherd, Jul 21 2002

Keywords

Examples

			0.42331082513074800310235591192...

Crossrefs

Cf. A059742 (Pi+e), A000796 (Pi), A001113 (e), A019609 (Pi*e), A061382 (Pi/e), A061360 (e/Pi), A039661 (e^Pi), A059850 (Pi^e), A073233 (Pi^Pi), A073226 (e^e), A049006 (i^i = e^(-Pi/2)).
Cf. A110564 for continued fraction for Pi - e.

Programs

A225155 Decimal expansion of Pi/(4*e) + e/(3*Pi).

Original entry on oeis.org

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

Views

Author

Jimmy Zotos, May 01 2013

Keywords

Comments

Approximates Euler Mascheroni constant giving 3 correct decimal places.
The constant is not known to be transcendental, or even irrational. - Balarka Sen, May 06 2013

Examples

			0.5773504972584854585501148923768706139231...

Links

Crossrefs

Cf. A000796, A001113, A061360, A086056, A001620, A225572 (continued fraction).

Programs

  • Magma
    R:= RealField(100); (3*Pi(R)^2 + 4*Exp(2))/(12*Pi(R)*Exp(1)); // G. C. Greubel, Aug 30 2018
  • Mathematica
    RealDigits[(3*Pi^2 + 4*E^2)/(12*E*Pi), 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)
  • PARI
    default(realprecision, 1020); x=10*Pi/exp(1)/4+10*exp(1)/Pi/3; d=0; for (n=0, 1000, d=floor(x); x=(x-d)*10; print1(d", ")) \\

Extensions

More terms from Balarka Sen, May 02 2013

A231097 Decimal expansion of the power tower of the ratio e/Pi.

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Nov 06 2013

Keywords

Comments

This infinite tetration limit of (e/Pi)^^n is also the only solution of x*(Pi/e)^x = 1.

Examples

			0.88036777898173462182674985...

Links

Crossrefs

Cf. A061360 (e/Pi), A231098 (tetration of Pi/e).

Programs

  • Mathematica
    RealDigits[ProductLog[Log[Pi] - 1]/(Log[Pi] - 1), 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)
  • PARI
    lambertw(log(Pi)-1)/(log(Pi)-1)

Formula

When 1/e^e <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).

A092159 Decimal expansion of (e/Pi)^5.

Original entry on oeis.org

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

Views

Author

Mohammad K. Azarian, Mar 31 2004

Keywords

Examples

			0.48497912546609

Links

Crossrefs

Cf. A061360, A092034.

Programs

  • Mathematica
    RealDigits[(E/Pi)^5, 10, 100][[1]] (* Vincenzo Librandi, Mar 01 2013 *)

A092160 Decimal expansion of (e/Pi)^3.

Original entry on oeis.org

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

Views

Author

Mohammad K. Azarian, Mar 31 2004

Keywords

Examples

			0.64778938568748...

Crossrefs

Cf. A061360, A092034.

Programs

  • Mathematica
    RealDigits[(E/Pi)^3,10,120][[1]] (* Harvey P. Dale, Oct 14 2012 *)

A092161 Decimal expansion of (e/Pi)^4.

Original entry on oeis.org

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

Views

Author

Mohammad K. Azarian, Mar 31 2004

Keywords

Examples

			.56050363937885

Links

Crossrefs

Cf. A061360, A092034.

Programs

  • Mathematica
    RealDigits[(E/Pi)^4, 10, 100][[1]] (* Vincenzo Librandi, Mar 01 2013 *)

A094127 Decimal expansion of (e/Pi)^(1/2).

Original entry on oeis.org

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

Views

Author

Mohammad K. Azarian, May 03 2004

Keywords

Examples

			0.93019136710263285866...

Crossrefs

Cf. A061360, A001113, A000796.

A094129 Decimal expansion of (e/Pi)^(1/3).

Original entry on oeis.org

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

Views

Author

Mohammad K. Azarian, May 03 2004

Keywords

Examples

			0.95290192232985715826466100...

Crossrefs

Cf. A061360, A001113, A000796.

Programs

  • Mathematica
    RealDigits[Surd[E/Pi,3],10,120][[1]] (* Harvey P. Dale, Aug 25 2016 *)
Showing 1-10 of 28 results. Next

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