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.

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A197847 Decimal expansion of least x having x^2+2x=4*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 20 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -1.6989977519984890831842928796985548...
greatest x: 0.88207436611847498021987395522394374915...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = 2; c = 4;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r1] (* A197847 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .88, .89}, WorkingPrecision -> 110]
RealDigits[r2] (* A197848 *)

A197848 Decimal expansion of greatest x having x^2+2x=4*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 20 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -1.6989977519984890831842928796985548...
greatest x: 0.88207436611847498021987395522394374915...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = 2; c = 4;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r1] (* A197847 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .88, .89}, WorkingPrecision -> 110]
RealDigits[r2] (* A197848 *)

A197849 Decimal expansion of least x having x^2-2x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 1.048558359490494095758565264045...
greatest x: 2.667028464105801792635542129...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -2; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 3}]
r1 = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
RealDigits[r1] (* A197849 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.6, 2.7}, WorkingPrecision -> 110]
RealDigits[r2] (* A197850 *)

A197850 Decimal expansion of greatest x having x^2-2x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 1.0485583594904940957585652640454931931...
greatest x: 2.66702846410580179263554212949839974

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -2; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 3}]
r1 = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
RealDigits[r1] (* A197849 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.6, 2.7}, WorkingPrecision -> 110]
RealDigits[r2] (* A197850 *)

A198098 Decimal expansion of least x having x^2-3x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 0.672255167738256880748604617870325976...
greatest x: 3.525867901227958617954825081711394...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -3; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 4}]
r1 = x /. FindRoot[f[x] == g[x], {x, .65, .68}, WorkingPrecision -> 110]
RealDigits[r1] (* A198098 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r2] (* A198099 *)

A198099 Decimal expansion of greatest x having x^2-3x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 0.672255167738256880748604617870325976...
greatest x: 3.525867901227958617954825081711394...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -3; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 4}]
r1 = x /. FindRoot[f[x] == g[x], {x, .65, .68}, WorkingPrecision -> 110]
RealDigits[r1] (* A198098 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r2] (* A198099 *)

A198100 Decimal expansion of least x having x^2-4x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 0.50130475545480646339369035756819...
greatest x: 4.222749528794927324484249676610...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -4; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 5}]
r1 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]
RealDigits[r1] (* A198100 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 4.2, 4.3}, WorkingPrecision -> 110]
RealDigits[r2] (* A198101 *)

A198101 Decimal expansion of greatest x having x^2-4x=-2*cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 0.50130475545480646339369035756819...
greatest x: 4.222749528794927324484249676610...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = -4; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 5}]
r1 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]
RealDigits[r1] (* A198100 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 4.2, 4.3}, WorkingPrecision -> 110]
RealDigits[r2] (* A198101 *)

A198102 Decimal expansion of least x having x^2+3x=cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -2.666509821525421471192909881243565...
greatest x: 0.2910714507806038010117661064073...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -3, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
RealDigits[r1] (* A198102 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .29, .3}, WorkingPrecision -> 110]
RealDigits[r2] (* A198103 *)

A198103 Decimal expansion of greatest x having x^2+3x=cos(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 21 2011

Keywords

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -2.666509821525421471192909881243565...
greatest x: 0.2910714507806038010117661064073...

Crossrefs

Cf. A197737.

Programs

  • Mathematica
    a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -3, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
RealDigits[r1] (* A198102 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .29, .3}, WorkingPrecision -> 110]
RealDigits[r2] (* A198103 *)
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