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 11-18 of 18 results.

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 *)

A196761 Decimal expansion of the least x>0 satisfying 3=x*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=6.7441683532591485558552811730153259440268799...

Crossrefs

Cf. A196765.

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Sin[x]}, {x, 0, 4 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[2/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196760 *)
t = x /. FindRoot[3/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196761 *)
t = x /. FindRoot[4/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196762 *)
t = x /. FindRoot[5/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196763 *)
t = x /. FindRoot[6/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196764 *)

A196763 Decimal expansion of the least x>0 satisfying 5=x*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=7.068891403395066800687599561916762042715045101700...

Crossrefs

Cf. A196765.

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Sin[x]}, {x, 0, 4 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[2/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196760 *)
t = x /. FindRoot[3/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196761 *)
t = x /. FindRoot[4/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196762 *)
t = x /. FindRoot[5/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196763 *)
t = x /. FindRoot[6/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196764 *)

A196764 Decimal expansion of the least x>0 satisfying 6=x*sin(x).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 06 2011

Keywords

Examples

			x=7.25663293662839986431355610086695712919471700...

Crossrefs

Cf. A196765.

Programs

  • Mathematica
    Plot[{1/x, 2/x, 3/x, 4/x, Sin[x]}, {x, 0, 4 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[2/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196760 *)
t = x /. FindRoot[3/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196761 *)
t = x /. FindRoot[4/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196762 *)
t = x /. FindRoot[5/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196763 *)
t = x /. FindRoot[6/x == Sin[x], {x, 6, 7}, WorkingPrecision -> 100]
RealDigits[t]   (* A196764 *)

A196621 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/3).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=1.0010650483255460284713072903054034845677614187490536443...

Crossrefs

Cf. A196625.

Programs

  • Mathematica
    Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196621 *)
t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196622 *)
t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196623 *)

A196622 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/4).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=1.03091534853511341186438401835343566209061693...

Programs

  • Mathematica
    Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196621 *)
t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196622 *)
t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196623 *)

A196623 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/5).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 05 2011

Keywords

Examples

			x=1.1604801436875870671464058599456358891754993473595...

Programs

  • Mathematica
    Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196621 *)
t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196622 *)
t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196623 *)

A009360 Expansion of e.g.f. log(1+sinh(x)*x) (even powers only).

Original entry on oeis.org

0, 2, -8, 126, -4248, 246250, -21819060, 2741961054, -463859694704, 101639490015186, -28002426109496940, 9474407274253732294, -3861976880978567739432, 1866672045348038810596026
Offset: 0

Views

Author

R. H. Hardin

Keywords

Links

Crossrefs

Cf. A133866.

Programs

  • Maple
    S:= series(log(1+sinh(x)*x),x,61):
seq(k!*coeff(S,x,k),k=0..60,2); # Robert Israel, Jan 04 2019
  • Mathematica
    Log[ 1+Sinh[ x ]*x ] (* Even Part *)

Formula

From Robert Israel, Jan 04 2019: (Start)
a(n) = [x^(2*n)] log(1+sinh(x)*x)*(2*n)!.
a(n) ~ (-1)^(n+1)*(2*n)!/(n*r^(2*n)) where r is the zero of x*sin(x)-1 near 1.114157 (see A133866). (End)

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997
Previous Showing 11-18 of 18 results.

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

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