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.

Previous Showing 11-19 of 19 results.

A334846 Decimal expansion of arclength between (0,1) and (1,sqrt(2)) on y^2 - x^2 = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 1.099687413739204296413721014223062752214344...

Crossrefs

Cf. A333202, A334847.

Programs

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

A334847 Decimal expansion of arclength between (0,1) and (sqrt(3),2) on y^2 - x^2 = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 2.03762235985767948861624584746725394131152...

Crossrefs

Cf. A333202, A334846.

Programs

  • Mathematica
    s = Integrate[Sqrt[1 + D[Sqrt[1 + x^2], x]^2], {x, 0, Sqrt[3]}]
r = N[s, 200]
RealDigits[r][[1]]

A334848 Decimal expansion of circumference of x^2 + 9 y^2 = 9.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 13.3648932205552582301295023250601962394009826...

Crossrefs

Cf. A093728, A249491, A333202, A334849.

Programs

  • Mathematica
    s = Integrate[Sqrt[D[ 3 Cos[t], t]^2 + D[Sin[t], t]^2], {t, 0, 2 Pi}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = 4*E(-8), where E = complete elliptic integral.
Equals 2*A093728 = 4*A249491.

A334849 Decimal expansion of circumference of 4 x^2 + 9 y^2 = 36.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 15.8654395892905897913316630277830724967300828483...

Crossrefs

Cf. A333202, A334848.

Programs

  • Mathematica
    s = Integrate[Sqrt[D[ 3 Cos[t], t]^2 + D[2 Sin[t], t]^2], {t, 0, 2 Pi}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = 8 E(-5/4), where E = complete elliptic integral.

A335996 Decimal expansion of the number u such that the arclength on y = x^2 from (0,0) to (u, u^2) is 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 04 2020

Keywords

Examples

			u = 0.763926663317091041161960918884092435074956...

Crossrefs

Cf. A333202.

Programs

  • Mathematica
    x = x /.FindRoot[1/2 x Sqrt[1 + 4 x^2] + 1/4 ArcSinh[2 x] == 1, {x, 0},    WorkingPrecision -> 200]
RealDigits[x][[1]]

A332632 Decimal expansion of arclength between (0,1) and (1,1/2) on y = 1/2^x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 12 2020

Keywords

Examples

			arclength = 1.1215531824007360312081857171447937526245255166...

Crossrefs

Cf. A333202, A332630.

Programs

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

A334844 Decimal expansion of arclength between (0,0) and (1,sin 1) on y = sin x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 1.311442498215547045545494653761965117948990...

Crossrefs

Cf. A333202, A334843.

Programs

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

Formula

arclength = sqrt(2)*E(1,1/2), where E = elliptic integral of the second kind.

A334845 Decimal expansion of arclength between (0,1) and (Pi/4,sqrt(2)) on y = sec x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 15 2020

Keywords

Examples

			arclength = 0.9246753483536079599958842623846196965880723284650...

Crossrefs

Cf. A333202, A332633.

Programs

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

A335998 Decimal expansion of the arclength on xy = 1 from (1,1) to (2,1/2).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jul 06 2020

Keywords

Examples

			u = 1.13209039330591770397227318699762818913452272138359826435...

Crossrefs

Cf. A333202.

Programs

  • Mathematica
    r = NIntegrate[Sqrt[1 + 1/x^4], {x, 1, 2}, WorkingPrecision -> 200]
RealDigits[r][[1]]
Previous Showing 11-19 of 19 results.

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

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