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 31 results. Next

A197701 Decimal expansion of Pi/(1 + 4*Pi).

Original entry on oeis.org

2, 3, 1, 5, 7, 2, 0, 7, 9, 4, 3, 7, 7, 0, 9, 7, 2, 1, 6, 0, 6, 2, 8, 9, 1, 1, 4, 5, 5, 1, 1, 3, 1, 2, 3, 0, 8, 9, 3, 0, 5, 4, 4, 3, 8, 1, 6, 8, 6, 5, 5, 2, 5, 2, 2, 8, 3, 8, 8, 4, 2, 4, 7, 9, 9, 2, 4, 0, 9, 7, 2, 9, 9, 7, 4, 0, 5, 9, 2, 3, 2, 7, 5, 6, 6, 1, 8, 4, 5, 6, 7, 2, 9, 1, 6, 5, 7, 3, 8
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=2*Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.2315720794377097216062891145511312308...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/2; c = 2*Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .23, .24}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197701 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, .8}]

A197724 Decimal expansion of Pi^2/(2 + Pi).

Original entry on oeis.org

1, 9, 1, 9, 5, 6, 1, 7, 1, 2, 8, 8, 6, 4, 7, 8, 6, 5, 9, 7, 0, 1, 4, 5, 2, 6, 0, 7, 3, 7, 1, 5, 6, 5, 1, 6, 0, 7, 2, 2, 3, 2, 4, 1, 3, 3, 4, 6, 2, 9, 2, 0, 2, 3, 0, 5, 5, 7, 1, 1, 1, 0, 4, 2, 2, 2, 2, 8, 8, 6, 7, 3, 8, 4, 1, 3, 5, 7, 7, 3, 2, 1, 3, 1, 3, 2, 9, 2, 0, 5, 8, 4, 2, 8, 7, 6, 8, 4, 5
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=1/2 and c=1/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.91956171288647865970145260737156516072232...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/2; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.9, 1.92}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197724 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2.8}]
RealDigits[Pi^2/(2+Pi),10,120][[1]] (* Harvey P. Dale, Mar 19 2023 *)

A197725 Decimal expansion of Pi^2/(4 + Pi).

Original entry on oeis.org

1, 3, 8, 1, 9, 8, 9, 2, 6, 7, 6, 3, 6, 0, 2, 2, 7, 4, 2, 1, 0, 4, 5, 5, 7, 8, 8, 5, 2, 2, 4, 6, 4, 9, 3, 4, 9, 0, 0, 0, 4, 1, 9, 6, 2, 6, 4, 2, 4, 3, 4, 8, 8, 5, 5, 9, 1, 1, 1, 4, 5, 1, 1, 9, 8, 0, 4, 4, 5, 5, 5, 5, 3, 9, 5, 0, 5, 9, 6, 6, 0, 7, 8, 8, 0, 6, 3, 2, 9, 9, 3, 5, 9, 4, 4, 1, 1, 7, 2
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=1/2 and c=2/Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.38198926763602274210455788522464934900041...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/2; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.37, 1.39}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197725 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2.8}]
RealDigits[Pi^2/(4+Pi),10,120][[1]] (* Harvey P. Dale, Jul 01 2013 *)

A197727 Decimal expansion of 2*Pi/(2+Pi).

Original entry on oeis.org

1, 2, 2, 2, 0, 3, 0, 9, 4, 0, 7, 0, 3, 3, 1, 4, 5, 7, 8, 7, 6, 1, 1, 9, 0, 7, 7, 5, 9, 0, 7, 9, 3, 7, 7, 2, 3, 4, 7, 4, 8, 4, 5, 2, 6, 5, 9, 1, 2, 1, 8, 5, 5, 9, 0, 4, 1, 7, 8, 3, 3, 5, 5, 0, 0, 8, 4, 9, 2, 9, 6, 6, 7, 8, 7, 2, 6, 3, 1, 6, 7, 7, 3, 1, 4, 7, 4, 2, 7, 6, 6, 9, 1, 3, 3, 4, 8, 6, 1
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=1/2 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
One-half of the harmonic mean of 2 and Pi. - Wesley Ivan Hurt, Sep 02 2014

Examples

			1.22203094070331457876119077590793772347484...

Links

Crossrefs

Cf. A197682.

Programs

  • Maple
    Digits:=100: evalf(2*Pi/(2+Pi)); # Wesley Ivan Hurt, Sep 02 2014
  • Mathematica
    b = 1/2; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.22, 1.23}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197727 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2}]

Formula

Continued fraction: 1 + 1/(4 + 3/(4 + 15/(4 + ... + (4*n^2 - 1)/(4 + ... )))). - Peter Bala, Feb 27 2024

A197728 Decimal expansion of 3*Pi/(2 + 2*Pi).

Original entry on oeis.org

1, 1, 3, 7, 8, 2, 0, 4, 8, 9, 4, 9, 2, 1, 6, 4, 2, 1, 8, 0, 1, 6, 6, 4, 6, 0, 3, 3, 5, 6, 7, 3, 3, 9, 2, 9, 6, 2, 0, 7, 6, 3, 9, 5, 4, 8, 4, 6, 0, 7, 9, 6, 4, 9, 5, 0, 0, 3, 4, 8, 2, 3, 2, 0, 6, 7, 3, 8, 2, 2, 2, 0, 5, 6, 5, 1, 4, 3, 6, 0, 6, 4, 4, 8, 0, 9, 4, 9, 7, 6, 1, 0, 2, 3, 0, 3, 3, 6, 5
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=1/3 and c=Pi/3; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.1378204894921642180166460335673392962076...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/3; c = Pi/3;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.137, 1.138}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197728 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197729 Decimal expansion of 3*Pi/(2 + Pi).

Original entry on oeis.org

1, 8, 3, 3, 0, 4, 6, 4, 1, 1, 0, 5, 4, 9, 7, 1, 8, 6, 8, 1, 4, 1, 7, 8, 6, 1, 6, 3, 8, 6, 1, 9, 0, 6, 5, 8, 5, 2, 1, 2, 2, 6, 7, 8, 9, 8, 8, 6, 8, 2, 7, 8, 3, 8, 5, 6, 2, 6, 7, 5, 0, 3, 2, 5, 1, 2, 7, 3, 9, 4, 5, 0, 1, 8, 0, 8, 9, 4, 7, 5, 1, 5, 9, 7, 2, 1, 1, 4, 1, 5, 0, 3, 7, 0, 0, 2, 2, 9, 1
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=1/3 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.8330464110549718681417861638619065852122678...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/3; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.83, 1.84}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197729 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi}]
RealDigits[3*Pi/(2+Pi),10,120][[1]] (* Harvey P. Dale, Jun 27 2015 *)

A197730 Decimal expansion of 3*Pi/(4+Pi).

Original entry on oeis.org

1, 3, 1, 9, 7, 0, 2, 5, 3, 9, 4, 6, 5, 3, 2, 7, 8, 7, 2, 2, 6, 8, 5, 6, 4, 1, 2, 3, 5, 4, 1, 1, 4, 0, 1, 5, 1, 3, 9, 7, 5, 6, 2, 3, 2, 9, 7, 1, 3, 0, 6, 7, 7, 2, 3, 7, 9, 7, 8, 4, 9, 6, 0, 4, 3, 7, 7, 5, 2, 0, 6, 3, 9, 2, 5, 1, 7, 0, 9, 2, 9, 3, 0, 6, 0, 5, 5, 1, 3, 7, 3, 8, 1, 0, 7, 7, 9, 0, 0
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=2/3 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			1.3197025394653278722685641235411401513975623...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 2/3; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.131, 1.132}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197730 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197731 Decimal expansion of 2*Pi/(1 + 4*Pi).

Original entry on oeis.org

4, 6, 3, 1, 4, 4, 1, 5, 8, 8, 7, 5, 4, 1, 9, 4, 4, 3, 2, 1, 2, 5, 7, 8, 2, 2, 9, 1, 0, 2, 2, 6, 2, 4, 6, 1, 7, 8, 6, 1, 0, 8, 8, 7, 6, 3, 3, 7, 3, 1, 0, 5, 0, 4, 5, 6, 7, 7, 6, 8, 4, 9, 5, 9, 8, 4, 8, 1, 9, 4, 5, 9, 9, 4, 8, 1, 1, 8, 4, 6, 5, 5, 1, 3, 2, 3, 6, 9, 1, 3, 4, 5, 8, 3, 3, 1, 4, 7, 6
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=1/4 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.463144158875419443212578229102262461786108876...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/4; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .46, .47}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197731 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, .8}]

A197732 Decimal expansion of 2*Pi/(1 + 2*Pi).

Original entry on oeis.org

8, 6, 2, 6, 9, 7, 4, 3, 8, 3, 0, 1, 5, 8, 7, 0, 2, 8, 8, 5, 3, 5, 8, 7, 6, 7, 4, 2, 9, 1, 3, 5, 0, 6, 6, 4, 7, 9, 5, 9, 0, 6, 4, 7, 1, 1, 9, 4, 3, 4, 6, 3, 0, 5, 2, 1, 2, 6, 1, 6, 2, 8, 4, 1, 9, 9, 5, 2, 5, 8, 2, 3, 3, 5, 5, 4, 4, 6, 2, 1, 2, 1, 4, 6, 4, 4, 1, 4, 1, 4, 8, 0, 4, 3, 7, 1, 8, 9, 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=1/4 and c=Pi/2; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.86269743830158702885358767429135066479590...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/4; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .86, .87}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197732 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197735 Decimal expansion of 3*Pi/(1 + Pi).

Original entry on oeis.org

2, 2, 7, 5, 6, 4, 0, 9, 7, 8, 9, 8, 4, 3, 2, 8, 4, 3, 6, 0, 3, 3, 2, 9, 2, 0, 6, 7, 1, 3, 4, 6, 7, 8, 5, 9, 2, 4, 1, 5, 2, 7, 9, 0, 9, 6, 9, 2, 1, 5, 9, 2, 9, 9, 0, 0, 0, 6, 9, 6, 4, 6, 4, 1, 3, 4, 7, 6, 4, 4, 4, 1, 1, 3, 0, 2, 8, 7, 2, 1, 2, 8, 9, 6, 1, 8, 9, 9, 5, 2, 2, 0, 4, 6, 0, 6, 7, 3, 1
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=1/6 and c=Pi/6; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			2.27564097898432843603329206713467859241...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 1/6; c = Pi/6;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 2.27, 2.28}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]   (* A197735 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi}]
Previous Showing 21-30 of 31 results. Next

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