A073233 -id:A073233 - cp's OEIS frontend

A331094 Decimal expansion of Pi^Pi - e^e.

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

Offset: 2

Ahmad J. Masad, Jan 08 2020

			21.30789736572864758123039575006221176...

Cf. A073233, A073226, A331189.

RealDigits[Pi^Pi - Exp[E], 10, 100][[1]] (* Amiram Eldar, Jan 09 2020 *)

Pi^Pi - exp(exp(1)) \\ Michel Marcus, Jan 09 2020

A331189 Decimal expansion of Pi^Pi + e^e.

Original entry on oeis.org

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

Offset: 2

Ahmad J. Masad, Jan 11 2020

			51.61642184868717596075...

Cf. A000796, A001113, A019314, A073233, A073226, A331094.

RealDigits[Pi^Pi + Exp[E], 10, 100][[1]] (* Amiram Eldar, Jan 11 2020 *)

Equals A073233 + A073226.

A161618 Engel expansion of Pi^Pi.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 7, 9, 23, 43, 128, 1847, 10674, 256943, 951850, 1361782, 1407741, 2143780, 3702054, 13341664, 17967518, 101541311, 159133300, 246184506, 3508330471

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 14 2009

nonn

			A073233 = 36.462... = 1/1 +1/1 +1/1 +... +1/(1*3) +1/(1*3*3) +1/(1*3*3*7) +1/(1*3*3*7*9) +...

Index to sequences related to Engel expansions

EngelExp[A_,n_]:=Join[Array[1&,Floor[A]],First@Transpose@NestList[ {Ceiling[1/Expand[ #[[1]]#[[2]]-1]],Expand[ #[[1]]#[[2]]-1 ]}&,{Ceiling[1/(A-Floor[A])], A-Floor[A]},n-1 ]]; EngelExp[N[Pi^Pi,7! ],50]

Example added by R. J. Mathar, Oct 02 2009

A220781 Decimal expansion of (log 2)^(log 2).

Original entry on oeis.org

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

Offset: 0

Jonathan Sondow, Dec 31 2012

A weak form of Schanuel's Conjecture implies that (log 2)^(log 2) is transcendental--see Marques and Sondow (2012).

			0.7756550370345751987332572790748780829226782575549514210453689950664279799102...

D. Marques and J. Sondow, The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture, arXiv:1212.6931 [math.NT], 2012-2013.

Cf. A073233 and its cross-refs.

RealDigits[ Log[2]^Log[2], 10, 200] [[1]]

cp's OEIS Frontend

A331094 Decimal expansion of Pi^Pi - e^e.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

A331189 Decimal expansion of Pi^Pi + e^e.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A161618 Engel expansion of Pi^Pi.

Views

Author

Keywords

Examples

Links

Programs

Mathematica

Extensions

A220781 Decimal expansion of (log 2)^(log 2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica