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 1-10 of 19 results. Next

A334843 Decimal expansion of arclength between (0,0) and (Pi/6,1/2) on y = sin x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.63397459621556135323627682924706381652859737309480968...

Links

Crossrefs

Cf. A333202, A332633, A334842.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Sin[x], x]^2], {x, 0, Pi/4}]
r = N[s, 200]
RealDigits[r][[1]]
  • PARI
    (3 - sqrt(3))/2 \\ Charles R Greathouse IV, Feb 11 2025

Formula

arclength = (3 - sqrt(3))/2.

A332633 Decimal expansion of arclength between (0,0) and (Pi/4,1) on y = tan x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.277978059277934418567056623029833449721770...

Crossrefs

Cf. A333202, A332634, A332635.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Tan[x], x]^2], {x, 0, Pi/4}]
r = N[s, 200]
RealDigits[r][[1]]

A333203 Decimal expansion of arclength from (0,0) to (1,1) on y = x^3.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.54786565468361014477533164606426061800663...

Crossrefs

Cf. A333202, A333204.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + 9 x^4], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
  • PARI
    intnum(x=0, 1, sqrt(1+9*x^4)) \\ Michel Marcus, Jun 12 2020

Formula

arclength = 2F1(-1/2;1/4;5/4;-9), where 2F1 is the hypergeometric function.

A332629 Decimal expansion of arclength between (0,1) and (1,e) on y = e^x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 2.003497111627352478569902752420239130821142795232094...

Crossrefs

Cf. A333202, A332630, A332631.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + E^(2 x)], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = sqrt(1 + e^2) - sqrt(2) + arctanh(sqrt(2)) - arctanh(sqrt(1+e^2)).

A332630 Decimal expansion of arclength between (0,1) and (1,2) on y = 2^x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.42116243743524518772746553679726129301339...

Crossrefs

Cf. A333202, A332629.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[2^x,x]^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

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.

A332631 Decimal expansion of arclength between (0,1) and (1,1/e) on y = 1/e^x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.192701401972154592777794219819503064418488768866...

Crossrefs

Cf. A333202, A332629.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[E^(-x), x]^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = sqrt(2) = sqrt(1+ 1/e^2) + arcsinh(e) - arcsinh(1).

A332634 Decimal expansion of arclength between (0,0) and (Pi/6,1) on y = tan x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.780131428280849333559981872217733063687522...

Crossrefs

Cf. A333202, A332633, A334843

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Tan[x], x]^2], {x, 0, Pi/6}]
r = N[s, 200]
RealDigits[r][[1]]

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]]

A334842 Decimal expansion of arclength between (0,0) and (Pi/3,sqrt(3)) on y = tan x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 2.056999740078724233251017930691409549645541986...

Crossrefs

Cf. A333202, A332633, A334843.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Tan[x], x]^2], {x, 0, Pi/3}]
r = N[s, 200]
RealDigits[r][[1]]
Showing 1-10 of 19 results. Next

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