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.

A382854 Decimal expansion of (1-log(2))/2.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Apr 06 2025

Keywords

Examples

			0.15342640972002734529138393927091171596224993281987...

References

  • Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (493), p. 313.

Links

Crossrefs

Cf. A187832, A372858, A382884.

Programs

  • Maple
    evalf[140]((1-log(2))/2);  # Alois P. Heinz, Apr 07 2025
  • Mathematica
    First[RealDigits[(1 - Log[2])/2, 10, 100]] (* Paolo Xausa, Apr 07 2025 *)
  • PARI
    (1-log(2))/2 \\ Amiram Eldar, Aug 01 2025

Formula

Equals Sum_{k>=1} (-1)^(k+1) / ((2*k-1) * 2*k * (2*k+1)).
Equals Sum_{k>=1} zeta(2*k)/((2*k+1)*4^k) (Srivastava and Choi, 2012). - Amiram Eldar, Aug 01 2025

A372859 Decimal expansion of (1 + log(4))/16.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 09 2024

Keywords

Examples

			0.149143397569993163677154015182272071009437516795031...

Links

Crossrefs

Cf. A372858, A372860, A372861.

Programs

  • Mathematica
    s = Integrate[Log[x]/x^3, {x, 2, Infinity}]
d = N[s, 100]
First[RealDigits[d]]
N[1/16  (1 + Log[4]), 100]
  • PARI
    (log(4)+1)/16 \\ Charles R Greathouse IV, Nov 21 2024

Formula

Equals Integral_{x=2..oo} log(x)/x^3 dx.

A372860 Decimal expansion of (1 + log(8))/72.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2024

Keywords

Examples

			0.04277002141221994344794022728297957922536806115389...

Links

Crossrefs

Cf. A372858, A372859, A372861.

Programs

  • Mathematica
    s = Integrate[Log[x]/x^4, {x, 2, Infinity}]
d = N[s, 100]
Join[{0},First[RealDigits[d]]]
N[1/72  (1 + Log[8]), 100]
  • PARI
    (log(8)+1)/72 \\ Charles R Greathouse IV, Nov 21 2024

Formula

Equals Integral_{x=2..oo} log(x)/x^4 dx.

A372861 Decimal expansion of (1 + log(16))/256.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2024

Keywords

Examples

			0.0147366746962491454596442518977840088761796895993...

Links

Crossrefs

Cf. A372858, A372859, A372860.

Programs

  • Mathematica
    s = Integrate[Log[x]/x^5, {x, 2, Infinity}]
d = N[s, 100]
Join[{0}, First[RealDigits[d]]]
N[1/256  (1 + Log[16]), 100]
  • PARI
    (log(16)+1)/256 \\ Charles R Greathouse IV, Nov 21 2024

Formula

Equals Integral_{x=2..oo} log(x)/x^5 dx.
Showing 1-4 of 4 results.

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