A049541 -id:A049541 - cp's OEIS frontend

A092748 Decimal expansion of Pi^(-8).

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

Offset: 0

Mohammad K. Azarian, Apr 12 2004

			0.000105390391653493666331...

Cf. A000796, A049541, A092736.

PadLeft[#1, Abs@ #2 + Length@ #1] & @@ RealDigits[Pi^(-8), 10, 102] (* Michael De Vlieger, Nov 16 2017 *)

{ default(realprecision, 20080); x=10*Pi^-8; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b092748.txt", n, " ", d)); } \\ Iain Fox, Nov 16 2017

PARI
```
1/Pi^8 \\ Michel Marcus, Nov 18 2017
```

A093204 Decimal expansion of Pi^(-1/3).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 22 2004

			0.682784063255295681467020833...

Index entries for transcendental numbers

Cf. A000796, A002161, A049541, A197111.

RealDigits[Surd[Pi,-3],10,120][[1]] (* Harvey P. Dale, Aug 18 2014 *)

PARI
```
Pi^(-1/3) \\ M. F. Hasler, Oct 07 2014
```

1/A092039. - M. F. Hasler, Oct 07 2014

A098801 Decimal expansion of Pi + 1/Pi.

Original entry on oeis.org

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

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Nov 01 2004

			3.45990253977358391000041091002453160826608869085601871847027928042561000155....

Index entries for transcendental numbers.

Cf. A000796, A049541.

RealDigits[Pi + 1/Pi, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Pi+1/Pi \\ Charles R Greathouse IV, Oct 02 2022

More terms from Ray Chandler, Nov 02 2004

A125560 Full solid angle of 4*Pi steradians (sr) in square degrees (degree^2).

Original entry on oeis.org

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

Offset: 5

Robert G. Wilson v, Dec 31 2006

"A 35 mm camera with a standard 50 mm lens covers an area some 38 degrees x 27 degrees. Theoretically, one can cover the sky with about 40 photographs." [A Field Guide]

One sphere = 4*Pi steradians, a spherical right angle = 1/4 hemisphere = 1/8 sphere = Pi/2 steradian.

			41252.96124941927103129467146615572263933194017592631151539537558... deg^2.
= 148510660.979093757126608172781606015015949846333347214554233520... min^2.
= 534638377792.473752565578942201378165405741944680004997239524067... sec^2.

John A. Adam, Mathematics in Nature, Modeling Pattern in the Natural World, Princeton University Press, Princeton & Oxford, 2003, page 78.
Patrick Kelly, Editor, Observer's Handbook 2007, The Royal Astronomical Society of Canada, page 32.
Donald H. Menzel, A Field Guide to the Stars and Planets, Houghton Mifflin Co., Boston, MA, 1964, page 317.

Rod Pierce, MathIsFun: Steradian, 2012.
Eric Weisstein's World of Mathematics, Solid Angle.
Wikipedia, Solid Angle.

Cf. A000796, A072097, A049541.

RealDigits[2^6*3^4*5^2/Pi, 10, 111][[1]]

129600/Pi \\ Charles R Greathouse IV, Nov 06 2017

4Pi*(180/Pi)^2 = 10*A019694*A072097^2 = 129600/Pi = 129600*A049541.

Definition changed to make it more rigorous by Stanislav Sykora, Nov 14 2013

A132698 Decimal expansion of 8/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007

			2.5464790894703253723021402139602297925513543318473031799626775049423487621476....

Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201.

Digits:=100; evalf(8/Pi); # Wesley Ivan Hurt, Mar 26 2014

RealDigits[N[8/Pi,6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

8/Pi \\ Charles R Greathouse IV, Oct 01 2022

More terms from Vladimir Joseph Stephan Orlovsky, Dec 02 2009

A132714 Decimal expansion of 24/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 31 2007

			=7.639437268410976116906420641880689377654062995541909539888032514827...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201, A132696 to A132699, A132701, A132702.

RealDigits[N[24/Pi,6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 03 2009 *)

PARI
```
24/Pi \\ G. C. Greubel, Feb 20 2017
```

24/Pi = Sum_{k>=0} ( (30*k+7)*C(2*k,k)^2*(Hypergeometric2F1[1/2 - k/2, -k/2, 1, 64])/(-256)^k ). - Alexander R. Povolotsky, Dec 20 2012

Another version of this identity is: Sum[(30*k+7) * Binomial[2k,k]^2 * (Sum[Binomial[k-m,m] * Binomial[k,m] * 16^m, {m,0,k/2}])/(256)^k, {k,0,infinity}]. - Alexander R. Povolotsky, Jan 25 2013

More terms from Vladimir Joseph Stephan Orlovsky, Dec 03 2009

A179706 Decimal expansion of e^(1/Pi).

Original entry on oeis.org

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

Offset: 1

Bronte Harkaitz (bronteharkaitz(AT)yahoo.com), Jul 25 2010

			e^(1/Pi) = 1.37480222743935863178...
1.3748022274... = 1 + A049541 + A092742/2! + A092743/3! + A092744/4! + A092745/5! + ... - _R. J. Mathar_, Jul 28 2010

Karl V. Keller, Jr., Table of n, a(n) for n = 1..1000

Cf. A001113 (decimal expansion of e, Euler's number), A000796 (decimal expansion of Pi).

x := exp(1)^(1/Pi) ; x := evalf(x) ; # R. J. Mathar, Jul 28 2010

RealDigits[N[E^(1/Pi),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

log(this number) = A049541. - R. J. Mathar, Jul 28 2010

Edited and extended by Klaus Brockhaus, Jul 29 2010

More digits from R. J. Mathar, Jul 28 2010

A232272 Decimal expansion of arctan(1/Pi).

Original entry on oeis.org

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

Offset: 0

Bruno Berselli, Nov 22 2013

			0.30816907111598493578699960803405309858963702926316931351366234390168...

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 35, page 338.

Cf. A019669, A049541, A232247, A232273.

Mathematica
```
RealDigits[ArcTan[1/Pi], 10, 90][[1]]
```

atan(1/Pi) \\ Charles R Greathouse IV, Nov 26 2024

Equals A019669 - A232273.
Equals Sum_{i>=0} (-1)^k/((1+2*k)*Pi^(1+2*k)).
From Wolfe Padawer, Feb 16 2023: (Start)
Equals arccot(Pi).
Equals arcsin(1/sqrt(Pi^2 + 1)).
Equals arccos(1/sqrt(1 + 1/Pi^2)). (End)

A337092 Decimal expansion of sqrt(40/Pi).

Original entry on oeis.org

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

Offset: 1

Peter Munn, Aug 15 2020

A gauge point marked c^1 or c_1 ("c" with a superscripted or subscripted "1") on slide rule calculating devices in the 20th century. The Pickworth reference notes its use "in calculating the contents of cylinders".

			3.568248232305...

C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London, 1945, p. 53, Gauge Points.

Peter Munn, Aristo 89 Slide Rule
Index entries for transcendental numbers

Cf. A002161, A010494, A190732.

evalf(sqrt(40.0/Pi)) ; # R. J. Mathar, Sep 02 2020

RealDigits[Sqrt[40/Pi], 10, 100][[1]] (* Amiram Eldar, Aug 15 2020 *)

sqrt(40/Pi) \\ Michel Marcus, Aug 19 2020

Equals A010494/A002161 = 2*sqrt(10*A049541).

A069985 Numerator of b(n) = binomial(2n,n)^3*(42n+5)/2^(12n+4).

Original entry on oeis.org

5, 47, 2403, 16375, 7417375, 53760105, 3167882487, 23607123111, 90865711740375, 687802362944125, 41879801005939325, 320193409525211313, 157265345845813485371, 1210756529837794953125, 74775114531441956109375, 578623856286382884714375, 18377920150990405063058370375

Offset: 0

Benoit Cloitre, May 01 2002

			Fractions begin with 5/16, 47/8192, 2403/33554432, 16375/17179869184, 7417375/562949953421312, 53760105/288230376151711744, ...

Amiram Eldar, Table of n, a(n) for n = 0..555
Srinivasa Ramanujan, Modular equations and approximations to Pi, Quart. J. Math., Vol. 45 (1914), pp. 350-372. See p. 45, eq. (29).

Cf. A049541, A069986 (denominators).

a[n_] := Numerator[Binomial[2 n, n]^3*(42 n + 5)/2^(12 n + 4)]; Array[a, 15, 0] (* Amiram Eldar, Apr 29 2022 *)

Sum_{n>=0} b(n) = 1/Pi (Ramanujan, 1914).

cp's OEIS Frontend

A092748 Decimal expansion of Pi^(-8).

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A093204 Decimal expansion of Pi^(-1/3).

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A098801 Decimal expansion of Pi + 1/Pi.

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A125560 Full solid angle of 4*Pi steradians (sr) in square degrees (degree^2).

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A132698 Decimal expansion of 8/Pi.

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Maple

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A132714 Decimal expansion of 24/Pi.

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A179706 Decimal expansion of e^(1/Pi).

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