A049541 -id:A049541 - cp's OEIS frontend

A073241 Decimal expansion of (1/Pi)^(1/Pi)^(1/Pi).

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

Offset: 0

Rick L. Shepherd, Jul 27 2002

			0.45150834553657280522199381804...

Cf. A000796 (Pi), A049541 (1/Pi), A073240 ((1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073242 (((1/Pi)^(1/Pi))^(1/Pi)), A073234 (Pi^Pi^Pi).

With[{c=1/Pi},RealDigits[c^c^c,10,120][[1]]] (* Harvey P. Dale, Mar 10 2015 *)

PARI
```
(1/Pi)^(1/Pi)^(1/Pi)
```

A165922 Decimal expansion of 2sqrt(3)/(9Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Sep 30 2009

The ratio of the volume of a regular tetrahedron to the volume of the circumscribed sphere. (The MathWorld link shows that the circumradius for a tetrahedron with side length a is a*sqrt(6)/4.)

			0.122517532315953788780294777402882098...

Frank Jackson and Eric W. Weisstein, Tetrahedron
Index entries for transcendental numbers

Cf. A000796, A002194, A010469, A049541, A020784.

RealDigits[(2Sqrt[3])/(9Pi),10,120][[1]] (* Harvey P. Dale, Nov 17 2013 *)

PARI
```
2*3^(-3/2)/Pi
```

2*sqrt(3)/(9*Pi) = A010469/(9*A000796) = (2/9)*A002194/A000796 = (2/9)*A002194*A049541 = 2*A020784/A000796 = 2*3^(-3/2)/Pi.

A092744 Decimal expansion of 1/Pi^4.

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 12 2004

			0.010265982254684335...

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A000796, A049541.

Join[{0},RealDigits[Pi^-4,10,120][[1]]] (* Harvey P. Dale, Jan 25 2013 *)

1/Pi^4 \\ Charles R Greathouse IV, Feb 28 2013

A138345 a(n) = -1 if (n+1)-st decimal digit of 1/Pi is smaller than n-th digit of 1/Pi, 0 if they are equal, 1 if larger.

Original entry on oeis.org

-1, 1, -1, -1, 1, -1, 0, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 0, -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, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 0, 1, -1, -1, 1, 0, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1

Offset: 1

Artur Jasinski, Mar 16 2008

Cf. A049541, A138344.

b = RealDigits[N[1/Pi, 1000]]; b = First[b]; a = {}; Do[k = b[[n + 1]] - b[[n]]; If[k < 0, AppendTo[a, -1], If[k == 0, AppendTo[a, 0], AppendTo[a, 1]]], {n, 1, 999}]; a (*Artur Jasinski*)
Which[#[[2]]<#[[1]],-1,#[[2]]==#[[1]],0,True,1]&/@ Partition[ RealDigits[ 1/Pi,10,110][[1]],2,1] (* Harvey P. Dale, Aug 09 2013 *)

A165953 Decimal expansion of (5sqrt(3) + sqrt(15))/(6Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Oct 02 2009

The ratio of the volume of a regular dodecahedron to the volume of the circumscribed sphere (which has circumradius a*(sqrt(3) + sqrt(15))/4 = a*(A002194 + A010472)/4, where a is the dodecahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165954. A063723 shows the order of these by size.

			0.6649088942053266431144284467086337161648765805556919381057592605722964718...

Eric Weisstein's World of Mathematics, Dodecahedron.
Index entries for transcendental numbers.

Cf. A000796, A002194, A010472, A165922, A049541, A165952, A165954, A063723, A002163, A020760, A010527.

RealDigits[(5*Sqrt[3]+Sqrt[15])/(6*Pi),10,120][[1]] (* Harvey P. Dale, Feb 16 2018 *)

PARI
```
(5*sqrt(3)+sqrt(15))/(6*Pi)
```

Equals (5*A002194 + A010472)/(6*A000796).
Equals (5*A002194 + A010472)*A049541/6.
Equals (10*A010527 + A010472)*A049541/6.
Equals (5 + sqrt(5))/(2*Pi*sqrt(3)).
Equals (5 + A002163)*A049541*A020760/2.

A165954 Decimal expansion of sqrt(10 + 2sqrt(5))/(2Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Oct 04 2009

The ratio of the volume of a regular icosahedron to the volume of the circumscribed sphere (with circumradius a*sqrt(10 + 2*sqrt(5))/4 = a*A019881, where a is the icosahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165953. A063723 shows the order of these by size.

			0.6054613829125255833862652051280444903008454088014288933200935000838295683...

Eric Weisstein's World of Mathematics, Icosahedron.
Index entries for transcendental numbers.

Cf. A000796, A002163, A165922, A049541, A165952, A165953, A063723, A019881, A019694, A060294.

RealDigits[Sqrt[10+2Sqrt[5]]/(2Pi),10,120][[1]] (* Harvey P. Dale, Aug 27 2013 *)

PARI
```
sqrt(10+2*sqrt(5))/(2*Pi)
```

sqrt(10 + 2*sqrt(5))/(2*Pi) = sqrt(10 + 2*A002163)/(2*A000796) = 2*sin(2*Pi/5)/Pi = 2*sin(A019694)/A000796 = 2*sin(72 deg)/Pi = 2*A019881/A000796 = 2*A019881*A049541 = (2/Pi)*sin(72 deg) = A060294*A019881.

A293009 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/Pi.

Original entry on oeis.org

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

Offset: 0

Alois P. Heinz, Mar 16 2018

			0.56501844596024150528994096062245192028392680078511838285519...

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Tetration

Cf. A000796, A049541, A073243, A277522, A277651, A300916.

RealDigits[Pi*Exp[-2*LambertW[Log[Pi]]]/(1+LambertW[Log[Pi]]), 10, 100][[1]] (* G. C. Greubel, Sep 09 2018 *)

Pi*exp(-2*lambertw(log(Pi)))/(1+lambertw(log(Pi))) \\ Michel Marcus, Mar 16 2018

Equals Pi*exp(-2*LambertW(log(Pi)))/(1+LambertW(log(Pi))).

A073239 Decimal expansion of (1/Pi)^Pi.

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 25 2002

(1/Pi)^Pi = Pi^(-Pi) = 1/(Pi^Pi) (reciprocal of A073233).

			0.02742569312329810611955627085...

Cf. A000796 (Pi), A049541 (1/Pi), A073238 (Pi^(1/Pi)), A073240 ((1/Pi)^(1/Pi)), A073233 (Pi^Pi).

Join[{0},RealDigits[(1/Pi)^Pi,10,120][[1]]] (* Harvey P. Dale, Nov 30 2011 *)

PARI
```
(1/Pi)^Pi
```

A092743 Decimal expansion of Pi^(-3).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 12 2004

			0.0322515344331994...

Index entries for transcendental numbers

Cf. A000796, A049541.

Join[{0},RealDigits[Pi^-3,10,120][[1]]] (* Harvey P. Dale, Oct 10 2012 *)

A092746 Decimal expansion of Pi^(-6).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 12 2004

			0.00104016147329585229...

Index entries for transcendental numbers

Cf. A000796, A049541, A092732, A092743.

evalf(1/Pi^6,100) ; # R. J. Mathar, May 12 2025

Join[{0,0},RealDigits[Pi^-6,10,120][[1]]] (* Harvey P. Dale, Aug 16 2016 *)

Equals A092743^2 = 1/A092732. - R. J. Mathar, May 12 2025

cp's OEIS Frontend

A073241 Decimal expansion of (1/Pi)^(1/Pi)^(1/Pi).

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A165922 Decimal expansion of 2*sqrt(3)/(9*Pi).

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A092744 Decimal expansion of 1/Pi^4.

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A138345 a(n) = -1 if (n+1)-st decimal digit of 1/Pi is smaller than n-th digit of 1/Pi, 0 if they are equal, 1 if larger.

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A165953 Decimal expansion of (5*sqrt(3) + sqrt(15))/(6*Pi).

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A165954 Decimal expansion of sqrt(10 + 2*sqrt(5))/(2*Pi).

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A293009 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/Pi.

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Mathematica

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Formula

A073239 Decimal expansion of (1/Pi)^Pi.

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A165922 Decimal expansion of 2sqrt(3)/(9Pi).

A165953 Decimal expansion of (5sqrt(3) + sqrt(15))/(6Pi).

A165954 Decimal expansion of sqrt(10 + 2sqrt(5))/(2Pi).