A019609 -id:A019609 - cp's OEIS frontend

A092141 Decimal expansion of (Pi*e)^5.

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

Offset: 5

Mohammad K. Azarian, Mar 30 2004

			45417.348166558...

Cf. A019609 (Pi*e), A092036 ((Pi*e)^2).

RealDigits[N[(Pi*E)^5,6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

A093443 Decimal expansion of (Pi*e)^(1/3).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, May 13 2004

			2.04400263596115084303020...

Cf. A000796, A001113, A019609.

RealDigits[N[(Pi E)^(1/3), 100]][[1]] (* Vincenzo Librandi, Aug 09 2015 *)
RealDigits[CubeRoot[Pi E],10,120][[1]] (* Harvey P. Dale, Dec 05 2023 *)

Offset corrected by Mohammad K. Azarian, Dec 11 2008

A093444 Decimal expansion of (Pi*e)^(1/4).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, May 13 2004

			1.709468445254921300

Cf. A000796, A001113, A019609.

RealDigits[N[(Pi E)^(1/4), 100]][[1]] (* Vincenzo Librandi, Aug 09 2015 *)

Offset corrected by Mohammad K. Azarian, Dec 11 2008

A094936 Decimal expansion of 2/(Pi*e).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Jun 18 2004

If N(n) denotes the number of real roots of the n-th Bernoulli polynomial then lim_{n->oo} N(n)/n = 2/(e*Pi).

			0.23419932609727664276...

A. P. Veselov and J.P. Ward, On the real roots of the Bernoulli polynomials and the Hurwitz zeta-function, 1999.
A. P. Veselov and J.P. Ward, On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials, J. Math. Anal. Appl. 305 (2) (2005) 712-721.

Cf. A000796 (Pi), A001113 (e), A019609, A019610.

RealDigits[2/(Pi*E), 10, 120][[1]] (* Amiram Eldar, Apr 28 2025 *)

2/exp(1)/Pi \\ Charles R Greathouse IV, Jan 14 2017

Equals 1/A019610. - Michel Marcus, Dec 07 2013

A096410 Decimal expansion of (Pi*e)^(-3).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Aug 07 2004

			0.001605709349794221049320880...

Cf. A000796, A001113, A019609.

Maple
```
evalf(1/(Pi^3*exp(3))) ;
```

Join[{0,0},RealDigits[(Pi*E)^-3,10,120][[1]]] (* Harvey P. Dale, Aug 19 2020 *)

A096412 Decimal expansion of (Pi*e)^(-1/3).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Aug 07 2004

			0.489236159683214034936711521614123...

Cf. A000796, A001113, A019609.

evalf(1/root[3](Pi*exp(1))) ; # R. J. Mathar, Oct 03 2011

A096413 Decimal expansion of (Pi*e)^(-1/4).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Aug 07 2004

			0.58497716221423254223842297737100...

Cf. A000796, A001113, A019609.

RealDigits[1/Surd[Pi*E,4],10,120][[1]] (* Harvey P. Dale, Jun 15 2018 *)

(Pi*exp(1))^(-1/4) \\ Michel Marcus, Apr 04 2020

Definition corrected by Georg Fischer, Apr 04 2020

A131567 Decimal expansion of 1/((ePiphi)^2).

Original entry on oeis.org

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

Offset: 0

Omar E. Pol, Aug 27 2007

phi=(5^(1/2) + 1)/2.

			0.005237644...

Cf. A001113, A000796, A001622, A019609, A094886, A094885.

Join[{0,0},RealDigits[1/(E*Pi*GoldenRatio)^2,10,120][[1]]] (* Harvey P. Dale, Sep 28 2015 *)

More terms from Harvey P. Dale, Sep 28 2015

A171819 Decimal expansion of 1/(2Pie).

Original entry on oeis.org

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

Offset: 0

Jonathan Vos Post, Oct 13 2010

This constant is the limit inferior of gamma(n)/n, gamma(n) being the n-dimensional Hermite constant. - Jean-François Alcover, May 21 2014

			0.05854983152431916069024226846666687221391492127606...

Eric Weisstein's World of Mathematics, Hermite Constants.

Cf. A001113 (e), A000796 (Pi), A019609 (Pi*e).

This is 1/2 of A096408 or the inverse of A019597.

RealDigits[1/(2*Pi*E), 10, 120, -1][[1]] (* Amiram Eldar, Jun 08 2023 *)

More terms from R. J. Mathar, Oct 15 2010

A225820 Decimal expansion of 1/(Pi - e).

Original entry on oeis.org

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

Offset: 1

K. D. Bajpai, Jul 30 2013

			2.3623303271092347498137623074013027750563468753752852179833394690014528...

Cf. A073244, A019609.

Mathematica
```
RealDigits[N[1/(Pi - E), 110]][[1]]
```

cp's OEIS Frontend

A092141 Decimal expansion of (Pi*e)^5.

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A093443 Decimal expansion of (Pi*e)^(1/3).

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A093444 Decimal expansion of (Pi*e)^(1/4).

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A094936 Decimal expansion of 2/(Pi*e).

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PARI

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A096410 Decimal expansion of (Pi*e)^(-3).

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Maple

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A096412 Decimal expansion of (Pi*e)^(-1/3).

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Maple

A096413 Decimal expansion of (Pi*e)^(-1/4).

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PARI

Extensions

A131567 Decimal expansion of 1/((e*Pi*phi)^2).

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Mathematica

Extensions

A171819 Decimal expansion of 1/(2*Pi*e).

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A131567 Decimal expansion of 1/((ePiphi)^2).

A171819 Decimal expansion of 1/(2Pie).