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 21-30 of 136 results. Next

A199966 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.943379571591794622084167020515639838...
greatest x: 2.3781281686737679859682016614728862...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
RealDigits[r]  (* A199965 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.37, 2.38}, WorkingPrecision -> 110]
RealDigits[r]  (* A199966 *)
  • PARI
    a=1; b=4; c=4; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A199967 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 3*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.45041223638324913376478190783839778...
greatest x: 0.989450014493949167489788332695714...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 2; b = 1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199967 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r]  (* A200003 *)
  • PARI
    a=2; b=1; c=3; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Extensions

A-number corrected by Jaroslav Krizek, Nov 27 2011

A200003 Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 3*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.45041223638324913376478190783839778...
greatest x: 0.989450014493949167489788332695714...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 2; b = 1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199967 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r]  (* A200003 *)
  • PARI
    a=2; b=1; c=3; solve(x=0.75, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200004 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.2841554251771481491680536288735443310...
greatest x: 1.36083225539066890467183928569132636...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 2; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
RealDigits[r]   (* A200004 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200005 *)
  • PARI
    a=2; b=1; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200005 Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.2841554251771481491680536288735443310...
greatest x: 1.36083225539066890467183928569132636...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 2; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
RealDigits[r]   (* A200004 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200005 *)
  • PARI
    a=2; b=1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200006 Decimal expansion of least x satisfying 3*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.31916558449395611450944828046123878...
greatest x: 0.9357819545602016906476903567483506551...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 3; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .31, .32}, WorkingPrecision -> 110]
RealDigits[r]  (* A200006 *)
r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
RealDigits[r]  (* A200007 *)
  • PARI
    a=3; b=1; c=4; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200007 Decimal expansion of greatest x satisfying 3*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.31916558449395611450944828046123878...
greatest x: 0.935781954560201690647690356748350...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 3; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .31, .32}, WorkingPrecision -> 110]
RealDigits[r]  (* A200006 *)
r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
RealDigits[r]  (* A200007 *)
  • PARI
    a=3; b=1; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Extensions

a(89)-a(98) corrected by G. C. Greubel, Jun 23 2018

A200008 Decimal expansion of least x satisfying 4*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.4039548562770990578793534464221104111...
greatest x: 0.5924702907925039329312822762880632483...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 4; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, .3, .7}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .40, .41}, WorkingPrecision -> 110]
RealDigits[r]  (* A200008 *)
r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]
RealDigits[r]  (* A200009 *)
  • PARI
    a=4; b=1; c=4; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200009 Decimal expansion of greatest x satisfying 4*x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  0.4039548562770990578793534464221104111...
greatest x: 0.59247029079250393293128227628806324...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 4; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, .3, .7}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .40, .41}, WorkingPrecision -> 110]
RealDigits[r]  (* A200008 *)
r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]
RealDigits[r]  (* A200009 *)
  • PARI
    a=4; b=1; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

A200010 Decimal expansion of least x satisfying x^2 - cos(x) = sin(x), negated.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 12 2011

Keywords

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x:  -0.560987729235911375277437028533668231799...
greatest x: 1.14955462727747318906952249474440902011...

Links

Crossrefs

Cf. A199949.

Programs

  • Mathematica
    a = 1; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200010 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]   (* A200011 *)
  • PARI
    a=1; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
Previous Showing 21-30 of 136 results. Next

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

Content is available under The OEIS End-User License Agreement.