A059850 -id:A059850 - cp's OEIS frontend

A114844 Sum of first n digits of Pi to digit-wise power of first n digits of e.

9, 10, 14, 15, 40, 43046761, 43046763, 44726379, 44726404, 44732965, 44733590, 44766358, 432186847, 432186848, 432193409, 432193652, 432193656, 432193683, 432226451, 432226515, 432273171, 432273172, 432273208, 432338744, 432340931

Offset: 1

Jonathan Vos Post, Feb 19 2006

The 331st digit of Pi and the 331st digit of e are both 0, so to generate any additional terms of the sequence beyond 330 terms one would have to define 0^0 to be either 0 or 1. - Harvey P. Dale, Aug 05 2014

			Since Pi =
3.1415926535897932384626433832795028841971693993751058209749445923078164062...
and e =
2.71828182845904523536028747135266249775724709369995957496696762772407663...
we have:
a(1) = 9 = 3^2.
a(2) = 10 = 3^2 + 1^7.
a(3) = 14 = 3^2 + 1^7 + 4^1.
a(4) = 15 = 3^2 + 1^7 + 4^1 + 1^8.
a(5) = 40 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2.
a(6) = 43046761 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2 + 9^8.

Harvey P. Dale, Table of n, a(n) for n = 1..300
Eric Weisstein's World of Mathematics, Pi Digits.
Eric Weisstein's World of Mathematics, e.

Cf. A000796, A001113, A039661, A059850, A114605.

With[{nn=30},Accumulate[RealDigits[Pi,10,nn][[1]]^RealDigits[E,10,nn] [[1]]]] (* Harvey P. Dale, Aug 05 2014 *)

a(n) = Sum_{i=1..n} A000796(i)^A001113(i).

A231738 Decimal expansion of (1/Pi)^(1/e).

Original entry on oeis.org

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

Offset: 0

Stanislav Sykora, Nov 13 2013

			0.6563096390202047074938345215400539960262419410006458186587329476836...

Stanislav Sykora, Table of n, a(n) for n = 0..5000

Cf. A205294 (inverse), A000796, A001113, A092171, A059850.

RealDigits[(1/Pi)^(1/E), 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

PARI
```
Pi^(-1.0/exp(1))
```

Equals Pi^(-1/e).

A092172 Decimal expansion of Pi^(-2*e).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 01 2004

			0.0019824994...

Cf. A059850.

Join[{0,0},RealDigits[Pi^(-2E),10,120][[1]]] (* Harvey P. Dale, Sep 24 2012 *)

A092174 Decimal expansion of Pi^(3e).

Original entry on oeis.org

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

Offset: 5

Mohammad K. Azarian, Apr 01 2004

			11328.70831...

Cf. A059850, A092173.

Digits:=100: evalf(Pi^(3*exp(1))); # Wesley Ivan Hurt, Jan 20 2017

RealDigits[Pi^(3E),10,120][[1]] (* Harvey P. Dale, Dec 22 2012 *)

Pi^(3*exp(1)) \\ Michel Marcus, Jan 21 2017

A277092 Decimal expansion of e^Pi/Pi^e.

Original entry on oeis.org

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

Offset: 1

Paulo Romero Zanconato Pinto, Sep 30 2016

			1.030345524216210832441552437544142391331167453542635047752...

Cf. A000796, A001113, A039661, A059850.

RealDigits[N[E^Pi/Pi^E, 120]] (* Michael De Vlieger, Sep 30 2016 *)

More digits from Jon E. Schoenfield, Mar 15 2018

A380965 Decimal expansion of the solution to e^(x+Pi) = Pi^(x+e).

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, Feb 09 2025

It would be nice to have a reference to the scientific literature for this number. - N. J. A. Sloane, Feb 11 2025

			0.2065517167786496639130717563086969850230914439...

Vicente, "x" approximate value?. [Posting to X, formerly Twitter. Author's name? Date?]

Cf. A000796, A001113, A039661, A053510, A059850, A179701.

RealDigits[(Pi-E Log[Pi])/(Log[Pi]-1),10,100][[1]]

Equals (Pi - e*log(Pi))/(log(Pi) - 1).

cp's OEIS Frontend

A114844 Sum of first n digits of Pi to digit-wise power of first n digits of e.

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A231738 Decimal expansion of (1/Pi)^(1/e).

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Mathematica

PARI

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A092172 Decimal expansion of Pi^(-2*e).

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A092174 Decimal expansion of Pi^(3e).

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Maple

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PARI

A277092 Decimal expansion of e^Pi/Pi^e.

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Extensions

A380965 Decimal expansion of the solution to e^(x+Pi) = Pi^(x+e).

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