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.

A192039 Decimal approximation of x such that f(x)=6, where f is the Fibonacci function described in Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[Pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			5.391849606901775521280408442083479799478829143140

Crossrefs

Cf. A192038.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == 6, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)

A192040 Decimal approximation of x such that f(x)=7, where f is the Fibonacci function described in Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			5.721461734953867596745254431493493958425727962366282

Crossrefs

Cf. A192038.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == 7, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)

A192041 Decimal approximation of x such that f(x)=1/2, where f is the Fibonacci function described in Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			0.450706666574544600230605063140328571518144024020

Crossrefs

Cf. A192038.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == 1/2, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)

A192042 Decimal approximation of x such that f(x)=3/2, where f is the Fibonacci function described in Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			2.50939491635468709205638984467935130148690741498451

Crossrefs

Cf. A192038.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == 3/2, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)

A192043 Decimal approximation of x such that f(x)=r, where f is the Fibonacci function described in Comments and r=(golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			2.6141654966507095222450798053609573198964859263002877

Crossrefs

Cf. A192038.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == r, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)

A192044 Decimal approximation of x such that f(x)=r+1, where f is the Fibonacci function described in Comments and r=(golden ratio).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jun 21 2011

Keywords

Comments

f(x)=(r^x-r^(-x*cos[pi*x]))/sqrt(5), where r=(golden ratio)=(1+sqrt(5))/2. This function, a variant of the Binet formula, gives Fibonacci numbers for integer values of x; e.g., f(3)=2, f(4)=3, f(5)=5.

Examples

			3.70822831961181544622795697604762903141444780151470467124724

Crossrefs

Cf. A192038, A104457.

Programs

  • Mathematica
    r = GoldenRatio; s = 1/Sqrt[5];
f[x_] := s (r^x - r^-x Cos[Pi x]);
x /. FindRoot[Fibonacci[x] == r+1, {x, 5}, WorkingPrecision -> 100]
RealDigits[%, 10]
(Show[Plot[#1, #2], ListPlot[Table[{x, #1}, #2]]] &)[
Fibonacci[x], {x, -7, 7}]
(* Peter J. C. Moses, Jun 21 2011 *)
Showing 1-6 of 6 results.

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