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 1-3 of 3 results.

A300707 Decimal expansion of Pi^4/96.

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Mar 11 2018

Keywords

Comments

Also the sum of the series Sum_{n>=0} (1/(2n+1)^4), whose value is obtained from zeta(4) given by L. Euler in 1735: Sum_{n>=0} (2n+1)^(-s) = (1-2^(-s))*zeta(s).
For the partial sums of this series see A120269/A128493. - Wolfdieter Lang, Sep 02 2019

Examples

			1.0146780316041920545462534655073449088513290174238064...

Links

Crossrefs

Cf. A013662, A092425, A111003, A120269, A128493, A300709, A300710, A300731.

Programs

  • MATLAB
    format long; pi^4/96
  • Maple
    evalf((1/96)*Pi^4, 120)
  • Mathematica
    RealDigits[Pi^4/96, 10, 120][[1]]
  • PARI
    default(realprecision, 120); Pi^4/96

Formula

Equals A092425/96. - Omar E. Pol, Mar 11 2018
Equals (15/16)*zeta(4) = (15/16)*A013662. - Wolfdieter Lang, Sep 02 2019
Equals Sum_{k>=1} 1/(2*k-1)^4. - Sean A. Irvine, Mar 25 2025
Equals lambda(4), where lambda is the Dirichlet lambda function. - Michel Marcus, Aug 15 2025

A016760 a(n) = (2*n+1)^8.

Original entry on oeis.org

1, 6561, 390625, 5764801, 43046721, 214358881, 815730721, 2562890625, 6975757441, 16983563041, 37822859361, 78310985281, 152587890625, 282429536481, 500246412961, 852891037441, 1406408618241, 2251875390625, 3512479453921, 5352009260481, 7984925229121, 11688200277601
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016756, A300710.

Programs

Formula

a(n) = A016756(n)^2. - Michel Marcus, Dec 26 2016
G.f.: -(1+6552*x +331612*x^2 +2485288*x^3 +4675014*x^4 +2485288*x^5 +331612*x^6 +6552*x^7 +x^8)/(x-1)^9 . - R. J. Mathar, Jul 07 2017
Sum_{n>=0} 1/a(n) = 17*Pi^8/161280 (A300710). - Amiram Eldar, Oct 11 2020
Product_{n>=1} (1 - 1/a(n)) = Pi*cosh(Pi/2)*(cos(Pi/sqrt(2)) + cosh(Pi/sqrt(2)))/32. - Amiram Eldar, Jan 28 2021

A300709 Decimal expansion of Pi^6/960.

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Mar 11 2018

Keywords

Comments

Also the sum of the series Sum_{n>=0} (1/(2n+1)^6), whose value is obtained from zeta(6) given by L. Euler in 1735: Sum_{n>=0}(2n+1)^(-s) = (1-2^(-s))*zeta(s).

Examples

			1.0014470766409421219064785871379373946533515917510902...

Links

Crossrefs

Cf. A092732, A111003, A300707, A300710.

Programs

  • MATLAB
    format long; pi^6/960
  • Maple
    evalf((1/960)*Pi^6, 120)
  • Mathematica
    RealDigits[Pi^6/960, 10, 120][[1]]
  • PARI
    default(realprecision, 120); Pi^6/960

Formula

Equals A092732/960. - Omar E. Pol, Mar 11 2018
From Artur Jasinski, Jun 24 2025: (Start)
Equals DirichletL(2,1,6).
Equals DirichletL(4,1,6).
Equals DirichletL(8,1,6).
Equals DirichletL(16,1,6). (End)
Showing 1-3 of 3 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.