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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A197690 Decimal expansion of Pi/(4 + 2*Pi).

Original entry on oeis.org

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

Examples

			0.30550773517582864469029769397698443086...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 2; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .3, .31}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197690 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

A197691 Decimal expansion of Pi/(4 + 4*Pi).

Original entry on oeis.org

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

Examples

			0.1896367482486940363361076722612232160346065914...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 2; c = 2 Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .1, .2}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197691 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi/(4+4Pi),10,120][[1]] (* Harvey P. Dale, Mar 19 2025 *)

A197692 Decimal expansion of (Pi^2)/(2+4*Pi).

Original entry on oeis.org

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

Examples

			0.6775609836097499310089623865334568879498040...

Links

Crossrefs

Cf. A197682.

Programs

  • Maple
    evalf((Pi^2)/(2+4*Pi),100); # Wesley Ivan Hurt, Feb 12 2017
  • Mathematica
    b = 2; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .6, .7}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197692 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]
  • PARI
    Pi^2/(2+4*Pi) \\ Michel Marcus, Feb 13 2017

A197693 Decimal expansion of (Pi^2)/(4+4*Pi).

Original entry on oeis.org

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

Examples

			x=0.59576141514875427327955317355865250501468575843...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 2; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .5, .6}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197693 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[Pi^2/(4+4*Pi),10,120][[1]] (* Harvey P. Dale, Nov 27 2022 *)

A197694 Decimal expansion of Pi/(4 + Pi).

Original entry on oeis.org

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

Examples

			0.4399008464884426240895213745137133837991874432...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 2; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .4, .45}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197694 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1.1}]

A197695 Decimal expansion of Pi/(6 + 2*Pi).

Original entry on oeis.org

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

Examples

			0.255763678152239207326144901069190024189115...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 3; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .2, .3}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197695 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, .4}]
RealDigits[Pi/(6+2*Pi),10,120][[1]] (* Harvey P. Dale, Jun 24 2015 *)

A197696 Decimal expansion of Pi/(6 + 4*Pi).

Original entry on oeis.org

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

Examples

			0.169208765614109593810546901991407567005009...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 3; c = 2*Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .15, .17}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]   (* A197696 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, .3}]

A197697 Decimal expansion of (Pi^2)/(2+6*Pi).

Original entry on oeis.org

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

Examples

			0.4733724036248419226997007643761582658652643123...

Links

Crossrefs

Cf. A197682.

Programs

  • Maple
    Digits:=100: evalf(Pi^2/(2+6*Pi)); # Wesley Ivan Hurt, Nov 08 2014
  • Mathematica
    b = 3; c = 1/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .15, .17}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197697 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi}]

A197698 Decimal expansion of Pi^2/(4 + 6*Pi).

Original entry on oeis.org

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

Examples

			0.43193856523863283370356856117136549702401320011...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 3; c = 2/Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .4, .5}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]   (* A197698 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2.5}]

A197699 Decimal expansion of Pi/(6 + Pi).

Original entry on oeis.org

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

Examples

			0.3436592257647935858831863748935727918327846776...

Links

Crossrefs

Cf. A197682.

Programs

  • Mathematica
    b = 3; c = Pi/2;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .34, .35}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197699 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1.5}]
Previous Showing 11-20 of 31 results. Next

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