A173163 -id:A173163 - cp's OEIS frontend

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

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

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

			2.5556046121008206152514542654716688251666246..

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

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

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

			2.6002950000539155877172082219411699164378377..

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

x=12;RealDigits[Log[x]/ProductLog[Log[x]],10,103][[1]]

A186503 Decimal expansion of the solution x to x^x = 13.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

			2.6410619164843958084118390040657912549308732...

Cf. A016636, A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186501, A186502, A186504, A344930, A093590.

x=13;RealDigits[Log[x]/ProductLog[Log[x]],10,103][[1]]
RealDigits[x/.FindRoot[x^x==13,{x,2.6},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Feb 07 2025 *)

Equals log(13)/LambertW(log(13)). - Alois P. Heinz, Jun 16 2021

A186504 Decimal expansion of the solution x to x^x = 14.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

			2.6785234858912995813011990010099506157786992..

Cf. A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186501, A186502, A186503, A344930, A093590.

x=14;RealDigits[Log[x]/ProductLog[Log[x]],10,200][[1]]
RealDigits[x/.FindRoot[x^x==14,{x,2},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Aug 08 2023 *)

A344930 Decimal expansion of the real solution to x^x = 15.

Original entry on oeis.org

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

Offset: 1

Christoph B. Kassir, Jun 02 2021

2.7131636040042392095764012768285093718781...

Cf. A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186501, A186502, A186503, A186504, A093590.

RealDigits[Log[15]/ProductLog[Log[15]], 10, 100][[1]] (* Amiram Eldar, Jun 02 2021 *)
RealDigits[x/.FindRoot[x^x==15,{x,2.7},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Apr 18 2022 *)

Equals log(15)/W(log(15)), where W(z) is the Lambert W Function.

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

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

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A186503 Decimal expansion of the solution x to x^x = 13.

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A186504 Decimal expansion of the solution x to x^x = 14.

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Mathematica

A344930 Decimal expansion of the real solution to x^x = 15.

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Formula