A061382 -id:A061382 - cp's OEIS frontend

A092158 Decimal expansion of (Pi/e)^5.

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

Offset: 1

Mohammad K. Azarian, Mar 31 2004

			2.0619444167600677

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A061382, A092035.

RealDigits[(Pi/E)^5, 10, 100][[1]] (* Vincenzo Librandi, Mar 01 2013 *)

A381845 a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ).

Original entry on oeis.org

1, 1, 8, 48, 192, 3840, 46080, 322560, 10321920, 26542080, 1857945600, 11678515200, 1961990553600, 25505877196800, 1428329123020800, 42849873690624000, 8903869857792000, 46620662575398912000, 2634762720116736000, 31888533201572855808000, 196237127394294497280000

Offset: 1

Stefano Spezia, Mar 12 2025

			1, 1, 7/8, 37/48, 133/192, 2431/3840, 27007/46080, 176761/322560, ...

Cf. A061360, A061382, A143991 (conjectured numerators).

a[n_]:=Denominator[(E/Pi)Integrate[Cos[x]/(1 + x^2)^n,{x,-Infinity,Infinity}]]; Array[a,21]

A096415 Decimal expansion of (Pi/e)^(1/3).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, Aug 07 2004

			1.04942594465019805059064435106277...

Cf. A000796, A001113, A061382.

RealDigits[N[(Pi/E)^(1/3), 110]][[1]] (* Georg Fischer, Apr 04 2020 *)

(Pi/exp(1))^(1/3) \\ Michel Marcus, Apr 04 2020

Definition corrected by Georg Fischer, Apr 04 2020

A096416 Decimal expansion of (Pi/e)^(1/4).

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, Aug 07 2004

			1.03684502385839719027416796694100...

Cf. A000796, A001113, A061382.

evalf(root[4](Pi/exp(1)) ; # R. J. Mathar, Oct 03 2011

equals the square root of A096414.

cp's OEIS Frontend

A092158 Decimal expansion of (Pi/e)^5.

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A381845 a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ).

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A096415 Decimal expansion of (Pi/e)^(1/3).

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A096416 Decimal expansion of (Pi/e)^(1/4).

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