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 25 results. Next

A003008 Number of n-level ladder expressions with A030798.

Original entry on oeis.org

1, 1, 2, 4, 8, 17, 39, 90, 213
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A082499.

A104748 Decimal expansion of solution to x*2^x = 1.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Mar 23 2005

Keywords

Comments

Writing the equation as (1/2)^x = x, the solution is the value of the infinite power tower function h(t) = t^t^t^... at t = 1/2. The solution is a transcendental number. - Jonathan Sondow, Aug 29 2011
Equals LambertW(log(2))/log(2) since, for 1/E^E <= c < 1, c^c^c^... = LambertW(log(1/c))/log(1/c). - Stanislav Sykora, Nov 03 2013

Examples

			x = 0.641185744504985984486200482114823666562820957191101... = (1/2)^(1/2)^(1/2)^...

Links

Crossrefs

Equals 1/A030798.
Cf. A073084.

Programs

  • Mathematica
    RealDigits[ ProductLog[ Log[2]]/Log[2], 10, 111][[1]] (* Robert G. Wilson v, Mar 23 2005 *)
RealDigits[x/.FindRoot[x 2^x==1,{x,.6},WorkingPrecision->100]][[1]] (* Harvey P. Dale, Apr 17 2019 *)
  • PARI
    lambertw(log(2))/log(2) \\ Stanislav Sykora, Nov 03 2013

Extensions

More terms from Robert G. Wilson v, Mar 23 2005
Offset corrected by R. J. Mathar, Feb 05 2009

A173158 Decimal expansion of x such that x^x=3.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			1.8254550229248300400414692977405862226338336459207140621453748035255....

Links

Crossrefs

Cf. A030798 (x^x=2), A103549.

Programs

  • Mathematica
    x=3;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]
  • PARI
    solve(x=1, 2, x^x-3) \\ Michel Marcus, Jan 14 2015
  • PARI
    log(3)/lambertw(log(3)) \\ Charles R Greathouse IV, Jul 14 2020

Formula

Equals log(3)/W(log(3)).
Equals 1/A103549. - Hugo Pfoertner, Apr 17 2024

A173159 Decimal expansion of the constant x which satisfies x^x = 5.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			2.12937248...^2.12937248... = 5.
2.12937248..*log(2.12937248..) = 1.609437... = A016628.

Links

Crossrefs

Cf. A030437, A030797, A030798, A173158.

Programs

  • Maple
    Digits := 20 ; fsolve(x^x=5) ; # R. J. Mathar, Mar 11 2010
  • Mathematica
    x=5;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]
  • PARI
    log(5)/lambertw(log(5)) \\ Charles R Greathouse IV, Jul 14 2020

Formula

Log(5)/W(log(5)).

Extensions

Keyword:cons added by R. J. Mathar, Mar 11 2010

A173160 Decimal expansion of the constant x satisfying x^x = 6.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			2.2318286..^2.2318286..=6. 2.2318286..*log(2.2318286..) = A016629.

Crossrefs

Cf. A030437, A030797, A030798, A173158, A173159.

Programs

  • Mathematica
    x=6;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]

Formula

Digits of log(6)/W(log(6)).

Extensions

Keyword:cons added by R. J. Mathar, Mar 14 2010

A173161 Decimal expansion of the solution x to x^x=7.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			2.3164549..^2.3164549..=7

Crossrefs

Cf. A030437, A030797, A030798, A173158, A173159, A173160.

Programs

  • Mathematica
    x=7;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]

Formula

Digits of log(7)/W(log(7)).

Extensions

Keyword:cons added by R. J. Mathar, Feb 13 2010

A173162 Decimal expansion of the solution x to x^x=8.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			2.3884234..^2.3884234..=8

Crossrefs

Cf. A030437, A030797, A030798, A173158-A173161.

Programs

  • Mathematica
    x=8;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]

Formula

Digits of log(8)/W(log(8)).

Extensions

Keyword:cons added by R. J. Mathar, Feb 13 2010

A173163 Decimal expansion of the solution x to x^x=9.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Examples

			2.450953928..^2.450953928..=9

Links

Crossrefs

Cf. A030437, A030797, A030798, A173158-A173162.

Programs

  • Mathematica
    x=9;RealDigits[Log[x]/ProductLog[Log[x]],10,6! ][[1]]

Formula

Digits of log(9)/W(log(9)).

Extensions

Keyword:cons added by R. J. Mathar, Feb 13 2010

A186501 Decimal expansion of the solution x to x^x = 11.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

Keywords

Examples

			2.5556046121008206152514542654716688251666246..

Crossrefs

Cf. A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186502, A186503, A186504, A344930, A093590.

Programs

  • Mathematica
    x=11;RealDigits[Log[x]/ProductLog[Log[x]],10,103][[1]]
RealDigits[x/.FindRoot[x^x==11,{x,2},WorkingPrecision->110]][[1]] (* Harvey P. Dale, Nov 13 2011 *)

A186502 Decimal expansion of the solution x to x^x = 12.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

Keywords

Examples

			2.6002950000539155877172082219411699164378377..

Crossrefs

Cf. A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186501, A186503, A186504, A344930, A093590.

Programs

  • Mathematica
    x=12;RealDigits[Log[x]/ProductLog[Log[x]],10,103][[1]]
Showing 1-10 of 25 results. Next

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