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 11-16 of 16 results.

A197005 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/3) orthogonally over the interval [0, 2*Pi] (as in A197004).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

See the Mathematica program for a graph.
xo=0.255465286103853596695882696613320272654788...
yo=0.264932084602776862434116494762571068650190...
m=1.0370570837365150046614795837584277605222343...
|OP|=0.3680373919265496189530095416155881110455...

Crossrefs

Cf. A197004, A197002, A196996, A197000.

Programs

  • Mathematica
    c = Pi/3;
xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197004 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197005 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
AspectRatio -> Automatic, AxesOrigin -> Automatic]

A197007 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/6) orthogonally over the interval [0, 2*Pi] (as in A197006).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

See the Mathematica program for a graph.
xo=0.460885580860965976987981282513698...
yo=0.553292712300593256734925495541442...
m=1.2004990723879979061250465124427113...
|OP|=0.7201030093885853693640956082816...

Crossrefs

Cf. A197006, A197002, A196996, A197000.

Programs

  • Mathematica
    c = Pi/6;
xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197006 *)
m = 1/Sin[xo + c]
RealDigits[m] (* A197007 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
AspectRatio -> Automatic, AxesOrigin -> Automatic]

A197009 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+1) orthogonally over the interval [0, 2*Pi] (as in A197006).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

See the Mathematica program for a graph.
xo=0.277097976418521518914833086895...
yo=0.289494183027862650094360757305...
m=1.0447358251025919644670467125044...
|OP|=0.4007370341535820008719293563...

Examples

			1.044735825102591964467046712504404113048658932805059578874283182084650....

Links

Crossrefs

Cf. A179378, A197002, A196996, A197000.

Programs

  • Mathematica
    c = 1;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A179378 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197009 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
AspectRatio -> Automatic, AxesOrigin -> Automatic]
  • PARI
    default(realprecision, 100); 1/sin(1 + solve(x=0, 2, x-sin(x+1)*cos(x+1))) \\ G. C. Greubel, Nov 16 2018

A197010 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=cos(x+1/2) orthogonally.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

See the Mathematica program for a graph.
xo=0.4672816053760121337816307268...
yo=0.5675398046001583628839615011...
m=1.21455627200105698029988016754...
|OP|=0.73515544514637791501789646...

Crossrefs

Cf. A179378, A197011, A197002, A196996, A197000.

Programs

  • Mathematica
    c = 1/2;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197010 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197011 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}],
 ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
 AspectRatio -> Automatic, AxesOrigin -> Automatic]

A197011 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+1/2) orthogonally over the interval [0, 2*Pi] (as in A197010).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 10 2011

Keywords

Comments

See the Mathematica program for a graph.
xo=0.4672816053760121337816307268...
yo=0.5675398046001583628839615011...
m=1.21455627200105698029988016754...
|OP|=0.73515544514637791501789646...

Crossrefs

Cf. A197010, A197002, A196996, A197000.

Programs

  • Mathematica
    c = 1/2;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197010 *)
m = 1/Sin[xo + c]
RealDigits[m]  (* A197011 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All,
AspectRatio -> Automatic, AxesOrigin -> Automatic]

A377479 Decimal expansion of the smallest positive real root of the equation cos(x) + x*sin(x) = 0.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Oct 29 2024

Keywords

Comments

The absolute value of the x-coordinate of the tangent point between the cosine graph and the straight line through the origin.

Examples

			2.79838604578388713672024890313957...

Links

Crossrefs

Cf. A003957, A115365, A197002, A377480, A377481.

Programs

  • Mathematica
    ndigits=100; First[RealDigits[First[x/.NSolve[Cos[x]+x Sin[x]==0,x,ndigits]],10,ndigits]]
(* or *)
RealDigits[BesselJZero[-3/2, 1], 10, 100][[1]] (* Vaclav Kotesovec, Oct 31 2024 *)
  • PARI
    \\ Note: besseljzero not guaranteed to work here since -3/2 < 0.
solve(x=2,3, cos(x)+x*sin(x)) \\ Charles R Greathouse IV, Jan 23 2025
Previous Showing 11-16 of 16 results.

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