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 31 results. Next

A197700 Decimal expansion of Pi/(1 + 2*Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/2 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.4313487191507935144267938371456753323979...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/2; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .43, .44}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197700 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]
RealDigits[Pi/(1+2 Pi),10,120][[1]] (* Harvey P. Dale, Mar 31 2023 *)
  • PARI
    1/(1/Pi+2) \\ Charles R Greathouse IV, Sep 30 2022

A197726 Decimal expansion of Pi/(1 + Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/2 and c=Pi/2; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.7585469929947761453444306890448928641384...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/2; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .75, .76}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197726 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2}]
  • PARI
    1/(1/Pi+1) \\ Charles R Greathouse IV, Sep 30 2022

A197686 Decimal expansion of Pi/(2 + Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x>0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1 and c=Pi/2; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.611015470351657289380595387953968861737422632...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .6, .7}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197686 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]

A197733 Decimal expansion of 2*Pi/(1+Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1/4 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
Equals the harmonic mean of 1 and Pi. - Stanislav Sykora, Apr 11 2016

Examples

			1.51709398598955229068886137808978572827685273...

Links

Crossrefs

Cf. A074950 (harmonic mean of Pi and e), A197682.

Programs

  • MATLAB
    2*pi/(1+pi) % Altug Alkan, Apr 11 2016
  • Mathematica
    b = 1/4; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.517, 1.518}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197733 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[2Pi/(1+Pi),10,120][[1]] (* Harvey P. Dale, Jun 17 2022 *)
  • PARI
    2*Pi/(1+Pi) \\ Michel Marcus, Apr 11 2016

A197683 Decimal expansion of Pi/(2+4*Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1 and c=2*pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			x=0.215674359575396757213396918572837666...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = 2*Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .2, .3}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197683 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi/(2+4Pi),10,120][[1]] (* Harvey P. Dale, Oct 27 2016 *)

A197684 Decimal expansion of Pi^2/(2 + 2*Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(bx) = cos(cx) (and also sin(cx) = cos(bx)), where b=1 and c=1/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.191522830297508546559106347117305010029371...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.1, 1.2}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197684 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

Extensions

Offset changed by Georg Fischer, Jul 29 2021

A197685 Decimal expansion of Pi^2/(4 + 2*Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(bx) = cos(cx) (and also sin(cx) = cos(bx)), where b=1 and c=2/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			x=0.9597808564432393298507263036857825803611620667...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .9, 1}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197685 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197687 Decimal expansion of 3*Pi/(6 + 2*Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=1 and c=Pi/3; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			x=0.7672910344567176219784347032075700725673464...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = Pi/3;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .7, .8}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197687 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197688 Decimal expansion of 2*Pi/(4+Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1 and c=pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
This number is the pressure drag coefficient for Kirchhoff flow past a plate, calculated by Kirchhoff (1969) for an infinitely long plate; see References. - Peter J. C. Moses and Clark Kimberling, Sep 07 2013

Examples

			x=0.8798016929768852481790427490274267675983748864...

References

  • Herbert Oertel and P. Erhard, Prandtl-Essentials of Fluid Mechanics, Springer, 2010, pages 163-164.

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .8, .9}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197688 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[(2 Pi)/(4+Pi),10,120][[1]] (* Harvey P. Dale, Dec 30 2023 *)
  • PARI
    2*Pi/(4+Pi) \\ Charles R Greathouse IV, Jul 22 2014

A197689 Decimal expansion of 3*Pi/(6 + Pi).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 17 2011

Keywords

Comments

Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=1 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			x=1.030977677294380757649559124680718375498354...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1, 1.05}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197689 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
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