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 1-6 of 6 results.

A196516 Decimal expansion of the number x satisfying x*e^x=3.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 03 2011

Keywords

Examples

			1.049908894964039959988697070552897904589...

Links

Programs

  • Mathematica
    Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A030175 *)
t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196515 *)
t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196516 *)
t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196517 *)
t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196518 *)
t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196519 *)
RealDigits[LambertW[3], 10, 50][[1]] (* _G. C. Greubel-, Nov 16 2017 *)
  • PARI
    lambertw(3) \\ G. C. Greubel, Nov 16 2017

A196517 Decimal expansion of the number x satisfying x*e^x=4.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 03 2011

Keywords

Examples

			1.2021678731970429392120741654951534475015125218296259...

Links

Programs

  • Mathematica
    Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A030175 *)
t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196515 *)
t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196516 *)
t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196517 *)
t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196518 *)
t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196519 *)
RealDigits[LambertW[4], 10, 50][[1]] (* G. C. Greubel, Nov 16 2017 *)
  • PARI
    lambertw(4) \\ G. C. Greubel, Nov 16 2017

A196518 Decimal expansion of the number x satisfying x*e^x=5.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 03 2011

Keywords

Examples

			1.32672466524220022363509929775807966012...

Links

Programs

  • Mathematica
    Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A030175 *)
t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196515 *)
t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196516 *)
t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196517 *)
t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196518 *)
t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196519 *)
RealDigits[LambertW[5], 10, 50][[1]] (* G. C. Greubel, Nov 16 2017 *)
  • PARI
    lambertw(5) \\ G. C. Greubel, Nov 16 2017

A196519 Decimal expansion of the number x satisfying x*e^x=6.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 03 2011

Keywords

Examples

			1.43240477589830031123407800721205869478643460...

Links

Programs

  • Mathematica
    Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A030175 *)
t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196515 *)
t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196516 *)
t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196517 *)
t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196518 *)
t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196519 *)
RealDigits[LambertW[6], 10, 50][[1]] (* G. C. Greubel, Nov 16 2017 *)
  • PARI
    lambertw(6) \\ G. C. Greubel, Nov 16 2017

Extensions

Terms a(95) onward corrected by G. C. Greubel, Nov 16 2017

A196549 Decimal expansion of the number x satisfying x*2^x=e.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 03 2011

Keywords

Examples

			x=1.19078368297329591531800250685857010...

Crossrefs

Cf. A196515.

Programs

  • Mathematica
    Plot[{2^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[2^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A104748 *)
t = x /. FindRoot[2^x == E/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196549 *)
t = x /. FindRoot[2^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196550 *)
t = x /. FindRoot[2^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196551 *)
t = x /. FindRoot[2^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196552 *)
t = x /. FindRoot[2^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196553 *)
RealDigits[ ProductLog[ E*Log[2] ] / Log[2], 10, 100] // First (* Jean-François Alcover, Feb 27 2013 *)

A364966 Decimal expansion of the solution to exp(-x^2) = x.

Original entry on oeis.org

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

Views

Author

Michal Paulovic, Aug 14 2023

Keywords

Comments

Fixed point of Gaussian function.

Examples

			0.6529186404192047...

Links

Crossrefs

Cf. A196515, A202498, A299624.

Programs

  • Maple
    Digits:=105: evalf(sqrt(LambertW(2)/2));
  • Mathematica
    RealDigits[Sqrt[ProductLog[2]/2], 10, 105][[1]]
  • PARI
    default(realprecision, 105); sqrt(lambertw(2)/2)

Formula

Equals sqrt(LambertW(2)/2).
Equals sqrt(A196515/2).
Equals sqrt(A202498).
Equals sqrt(A299624)/2.
Showing 1-6 of 6 results.

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