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.

A346933 Decimal expansion of 2 * Pi^2 / 27.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Aug 07 2021

Keywords

Examples

			0.73108180748810063843218451850...

References

  • L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).

Links

Crossrefs

Cf. A346932, A346931, A346930, A346929.

Programs

  • Mathematica
    RealDigits[(2 Pi^2)/27,10,120][[1]] (* Harvey P. Dale, Dec 04 2022 *)

Formula

Equals 2 * Pi^2 / 3^3.
Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^2 + (-1)^k/(3*k+1)^2 ).
Equals Integral_{0..infinity} x * log(x) / (x^3+1) dx.
Equals Integral_{0..1} (1+x) * log(x) / (1-x^3) dx.
Equals Integral_{0..infinity} x * (1-exp(-x)) / (exp(x) * (1+exp(-3*x))) dx.

A346929 Decimal expansion of 73 * Pi^10 / 4591650240.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Aug 07 2021

Keywords

Examples

			0.999022588776486297953644795760380979559997526690...

References

  • L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).

Links

Crossrefs

Cf. A346933, A346932, A346931, A346930.

Programs

  • Mathematica
    RealDigits[73 * Pi^10 / 4591650240, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Formula

Equals 11 * 61 * 73 * Pi^10 / (2^6 * 3^15 * 5).
Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^10 + (-1)^k/(3*k+1)^10 ).

A346930 Decimal expansion of 5207 * Pi^8 / 49601160.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Aug 07 2021

Keywords

Examples

			0.9960811602123716230652366325473543260...

References

  • L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).

Links

Crossrefs

Cf. A346933, A346932, A346931, A346929.

Programs

  • Mathematica
    RealDigits[5207 * Pi^8 / 49601160, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Formula

Equals 41 * 127 * Pi^8 / (2^3 * 3^11 * 5 * 7).
Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^8 + (-1)^k/(3*k+1)^8 ).

A346932 Decimal expansion of 7 * Pi^4 / 729.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Aug 07 2021

Keywords

Examples

			0.9353410661701194247669167747886636196818835386951960...

References

  • L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).

Links

Crossrefs

Cf. A346933, A346931, A346930, A346929.

Programs

  • Mathematica
    RealDigits[7 * Pi^4 / 729, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Formula

Equals 7 * Pi^4 / 3^6.
Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^4 + (-1)^k/(3*k+1)^4 ).
Showing 1-4 of 4 results.

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