cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A228824 Decimal expansion of 4*Pi/5.

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Oct 03 2013

Keywords

Comments

With offset 2, decimal expansion of 8*Pi.
8*Pi is also the surface area of a sphere whose diameter equals the square root of 8, hence its radius equals the square root of 2. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Dec 18 2013

Examples

			4*Pi/5 = 2.5132741228718345907701147066236023073577...
8*Pi = 25.132741228718345907701147066236023073577...

Links

Crossrefs

Cf. A002193, A228819.
Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721 (Pi through 7*Pi).

Programs

A229939 Decimal expansion of 9*Pi/10.

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Oct 06 2013

Keywords

Comments

With offset 2, decimal expansion of 9*Pi.
9*Pi is also the surface area of a sphere whose diameter equals the square root of 9. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Dec 22 2013

Examples

			9*Pi/10 = 2.827433388230813914616379044951552595777...
9*Pi = 28.27433388230813914616379044951552595777...

Links

Crossrefs

Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721, A228824 (Pi through 8*Pi).

Programs

Formula

9*Pi = Sum_{j >= 0} j*(j - 1)*(j - 2)*(j - 3)*2^(j+1) / ((2*j + 1)*binomial(2*j, j)). - Peter Bala, Nov 21 2023

A347152 Decimal expansion of 7 * Pi / 2.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Aug 19 2021

Keywords

Examples

			10.995574287564276334619251841478260094690...

Links

Crossrefs

Cf. A019669, A197723, A003881.

Programs

Formula

Equals A228721/2. - R. J. Mathar, Mar 11 2025

A265729 Decimal expansion of 32*Pi.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein and Robert G. Wilson v, Dec 14 2015

Keywords

Comments

"The integral corresponds to integration over a spherical cone with opening angle Pi/2 and radius 4. However, it is not clear what the integrand physically represents (it resembles computation of a moment of inertia, but that would give a factor (rho*sin(phi))^2 rather than the given rho*cos(phi))."

Examples

			100.53096491487338363080458826494409229430942078000338627119822695385012500...

References

  • The Jun 02 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007)

Links

Crossrefs

Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721, A228824, A229939, A061146.

Programs

  • Mathematica
    RealDigits[32 Pi, 10, 111][[1]] (* or *)
Integrate[\[Rho] Cos[\[Phi]] \[Rho]^2 Sin[\[Phi]], {\[Rho], 0, 4}, {\[Phi], 0, Pi/4}, {\[Theta], 0, 2 Pi}]
  • PARI
    32*Pi \\ Altug Alkan, Dec 14 2015

Formula

Equals Integral_{theta=0..2*Pi} Integral_{phi=0..Pi/4} Integral_{rho=0..4} (rho*cos(phi))*rho^2*sin(phi) d(rho) d(phi) d(theta).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.