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 1-6 of 6 results.

A196617 Decimal expansion of the least x>0 satisfying 1 = (x^2)*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Comments

This number is the least x>0 for which there exists a constant c such that the graph of y=cos(x) is tangent to the graph of the hyperbola y=(1/x)-c, as indicated by the graph in the Mathematica program.

Examples

			1.0682235441972490182834711142630928984689...

Links

Crossrefs

Cf. A196619, A196612.

Programs

  • Mathematica
    Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt]      (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c]       (* A196619 *)
slope = -Sin[xt]
RealDigits[slope]   (* A196620 *)
  • PARI
    a=1; c=0; solve(x=1, 1.5, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Extensions

Terms a(88) onward corrected by G. C. Greubel, Aug 22 2018

A196613 Decimal expansion of the least x>0 satisfying 3*sec(x)=x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=5.31246971165656769736615799825440318119169412292...

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Cos[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[2/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196612 *)
t = x /. FindRoot[3/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196613 *)
t = x /. FindRoot[4/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196614 *)
t = x /. FindRoot[5/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]    (* A196615 *)
t = x /. FindRoot[6/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196616 *)

A196614 Decimal expansion of the least x>0 satisfying 4*sec(x)=x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=5.5224341025910269165127934771802264618...

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Cos[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[2/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196612 *)
t = x /. FindRoot[3/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196613 *)
t = x /. FindRoot[4/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196614 *)
t = x /. FindRoot[5/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]    (* A196615 *)
t = x /. FindRoot[6/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196616 *)

A196615 Decimal expansion of the least x>0 satisfying 5*sec(x)=x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=5.762809456090988033007300152999953356676...

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Cos[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[2/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196612 *)
t = x /. FindRoot[3/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196613 *)
t = x /. FindRoot[4/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196614 *)
t = x /. FindRoot[5/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]    (* A196615 *)
t = x /. FindRoot[6/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196616 *)

A196616 Decimal expansion of the least x>0 satisfying 6*sec(x)=x.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=6.7626979446825445009979360144608109491765883176...

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Cos[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[2/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196612 *)
t = x /. FindRoot[3/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196613 *)
t = x /. FindRoot[4/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A196614 *)
t = x /. FindRoot[5/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]    (* A196615 *)
t = x /. FindRoot[6/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196616 *)

A196619 Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x = 0.454451866354226599819691146329523402836346961...

Links

Crossrefs

Cf. A196617, A196618, A196620, A196612.

Programs

  • Mathematica
    Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt]      (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c]       (* A196619 *)
slope = -Sin[xt]
RealDigits[slope]   (* A196620 *)
  • PARI
    a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); 1/x - cos(x) \\ G. C. Greubel, Aug 22 2018
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.