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.

A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 13 2020

Keywords

Examples

			Equals 1.478942857544597433827906...

Links

Crossrefs

Cf. A333203, A333204, A335996.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
  • PARI
    sqrt(5)/2 + asinh(2)/4 \\ Charles R Greathouse IV, Sep 02 2024

Formula

arclength = (2 sqrt(5) + arcsinh(2))/4.
arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.

A333204 Decimal expansion of arclength from (0,0) to (1,1) on y = x^4.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.60022942767220583728997791564995...

Crossrefs

Cf. A333202, A333203.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + 16 x^6], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = 2F1(-1/2;1/6;7/6;-16), where 2F1 is the hypergeometric function.

A333205 Decimal expansion of arclength between inflection points of y = 1/(1 + x^2).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.2764850435772190795057881032652202089789823679976841...

Crossrefs

Cf. A333202, A333203.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + 4 x^2/(1 + x^2)^4], {x, -Sqrt[1/3], Sqrt[1/3]}]
r = N[s, 200]
RealDigits[r][[1]]
Showing 1-3 of 3 results.

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

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