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 158 results. Next

A200614 Decimal expansion of the lesser of two values of x satisfying 3*x^2 - 1 = tan(x) and 0 < x < Pi/2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 20 2011

Keywords

Comments

For many choices of a and c, there are exactly two values of x satisfying a*x^2 - c = tan(x) and 0 < x < Pi/2; for other choices, there is exactly once such value.
Guide to related sequences, with graphs included in Mathematica programs:
a.... c.... x
3.... 1.... A200614, A200615
4.... 1.... A200616, A200617
5.... 1.... A200620, A200621
5.... 2.... A200622, A200623
5.... 3.... A200624, A200625
5.... 4.... A200626, A200627
5... -1.... A200628
5... -2.... A200629
5... -3.... A200630
5... -4.... A200631
6.... 1.... A200633, A200634
6.... 5.... A200635, A200636
6... -1.... A200637
6... -5.... A200638
1... -5.... A200639
2... -5.... A200640
3... -5.... A200641
4... -5.... A200642
2.... 0.... A200679, A200680
3.... 0.... A200681, A200682
4.... 0.... A200683, A200684
5.... 0.... A200618
6.... 0.... A200632
7.... 0.... A200643
8.... 0.... A200644
9.... 0.... A200645
10... 0.... A200646
-1... 1.... A200685
-1... 2.... A200686
-1... 3.... A200687
-1... 4.... A200688
-1... 5.... A200689
-1... 6.... A200690
-1... 7.... A200691
-1... 8.... A200692
-1... 9.... A200693
-1... 10... A200694
-2... 1.... A200695
-2... 3.... A200696
-3... 1.... A200697
-3... 2.... A200698
-4... 1.... A200699
-5... 1.... A200700
-6... 1.... A200701
-7... 1.... A200702
-8... 1.... A200703
-9... 1.... A200704
-10.. 1.... A200705
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0. We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A200614, take f(x,u,v) = u*x^2 - v = tan(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0. If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous. A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

Examples

			lesser:  0.839582259045302941513764008863804986308...
greater: 1.350956593976519397744696294368524715373...

Links

Crossrefs

Cf. A200615, A200338.

Programs

  • Mathematica
    (* Program 1:  A200614 and A200615 *)
a = 3; c = 1;
f[x_] := a*x^2 - c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
RealDigits[r]   (* A200614 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200615 *)
(* Program 2: implicit surface of u*x^2-v=tan(x) *)
f[{x_, u_, v_}] := u*x^2 - v - Tan[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 1.55}]}, {u, 1, 20}, {v, -20, 0}];
ListPlot3D[Flatten[t, 1]]  (* for A200614 *)

A200339 Decimal expansion of least x>0 satisfying x^2+2=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.30747760030134992121693507169004808...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 0; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200339 *)
  • PARI
    solve(x=1,1.5,x^2+2-tan(x)) \\ Charles R Greathouse IV, Mar 23 2022

A200340 Decimal expansion of least x>0 satisfying x^2+3=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.36837127504789773408079088664042065...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 0; c = 3;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]  (* A200340 *)
  • PARI
    solve(x=1,1.4,x^2+3-tan(x)) \\ Charles R Greathouse IV, Mar 23 2022

A200341 Decimal expansion of least x>0 satisfying x^2+4=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.4049378963781757888235227493280053174...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 0; c = 4;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200341 *)

A200342 Decimal expansion of least x>0 satisfying x^2+x+1=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.331891417552288203767329149758089201...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 1; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200342 *)

A200343 Decimal expansion of least x>0 satisfying x^2+x+2=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.384333986079017101143121947794272497000...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200343 *)

A200344 Decimal expansion of least x>0 satisfying x^2+x+3=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.41632970423011263898244065163005347571...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200344 *)

A200345 Decimal expansion of least x>0 satisfying x^2+x+4=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.438371935323166343024711233387578921848390...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200345 *)

A200346 Decimal expansion of least x>0 satisfying x^2+2x+1=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.398718475971114804506725257228099498174...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 2; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200346 *)

A200347 Decimal expansion of least x>0 satisfying x^2+2x+2=tan(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Nov 16 2011

Keywords

Comments

See A200338 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=1.4266351099330438090149257114961043442497281...

Crossrefs

Cf. A200338.

Programs

  • Mathematica
    a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200347 *)
Showing 1-10 of 158 results. Next

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