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 1-5 of 5 results.

A196772 Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0 < x < 2*Pi; c = Pi - sqrt(r) - arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			c=0.965016109773342910082904125880052671050...

Crossrefs

Cf. A195625, A196767.

Programs

  • Mathematica
    Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]
r = GoldenRatio; x = Sqrt[r];
c = N[Pi - x - ArcCos[r - 1], 100]
RealDigits[c]      (* A196772 *)
slope = N[-1/x^2, 100]
RealDigits[slope]  (* 1-r *)

A196768 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/3).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=1.6833055867088961454373617589948556354513948660...

Crossrefs

Cf. A196772.

Programs

  • Mathematica
    Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)

A196769 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/4).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=1.5095068322244728855653262204377685055328808170667196...

Crossrefs

Cf. A196772.

Programs

  • Mathematica
    Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)

A196770 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/5).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=1.41392254090929674042445333303603311304090191571000...

Crossrefs

Cf. A196772.

Programs

  • Mathematica
    Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)

A196771 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/6).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=1.354287214157721417830637161637530685977263257675514...

Crossrefs

Cf. A196772.

Programs

  • Mathematica
    Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)
Showing 1-5 of 5 results.

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