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 1-3 of 3 results.

A293418 a(n) is the greatest integer k such that k/Fibonacci(n) < sqrt(2).

Original entry on oeis.org

0, 1, 1, 2, 4, 7, 11, 18, 29, 48, 77, 125, 203, 329, 533, 862, 1395, 2258, 3654, 5912, 9567, 15479, 25047, 40527, 65574, 106101, 171675, 277776, 449452, 727229, 1176682, 1903911, 3080594, 4984506, 8065100, 13049606, 21114706, 34164312, 55279018, 89443331
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2017

Keywords

Links

Crossrefs

Cf. A000045, A293419, A293420.

Programs

  • Magma
    [Floor(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018
  • Mathematica
    z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293418 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293420 *)
  • PARI
    for(n=0,30, print1(floor(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

Formula

a(n) = floor(Fibonacci(n)*sqrt(2)).
a(n) = A293419(n) - 1 for n > 0.

A293420 a(n) is the integer k that minimizes |k/Fibonacci(n) - sqrt(2)|.

Original entry on oeis.org

0, 1, 1, 3, 4, 7, 11, 18, 30, 48, 78, 126, 204, 330, 533, 863, 1396, 2258, 3654, 5913, 9567, 15480, 25047, 40527, 65574, 106101, 171676, 277777, 449453, 727230, 1176682, 1903912, 3080594, 4984506, 8065100, 13049606, 21114706, 34164312, 55279019, 89443331
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2017

Keywords

Links

Crossrefs

Cf. A000045, A293418, A293419.

Programs

  • Magma
    [Round(Fibonacci(n)*Sqrt(2)): n in [0..30]]; // G. C. Greubel, Feb 08 2018
  • Mathematica
    z = 120; r = Sqrt[2]; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A293418 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A293419 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293420 *)
  • PARI
    for(n=0,30, print1(round(fibonacci(n)*sqrt(2)), ", ")) \\ G. C. Greubel, Feb 08 2018

Formula

a(n) = floor(1/2 + Fibonacci(n)*sqrt(2)).
a(n) = A293418(n) if (fractional part of Fibonacci(n)*sqrt(2)) < 1/2, otherwise a(n) = A293419(n).

A293505 a(n) is the integer k that minimizes |k/Fibonacci(n) - 1/2|.

Original entry on oeis.org

0, 0, 0, 1, 2, 2, 4, 6, 10, 17, 28, 44, 72, 116, 188, 305, 494, 798, 1292, 2090, 3382, 5473, 8856, 14328, 23184, 37512, 60696, 98209, 158906, 257114, 416020, 673134, 1089154, 1762289, 2851444, 4613732, 7465176, 12078908, 19544084, 31622993, 51167078
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2017

Keywords

Links

Crossrefs

Cf. A000045, A004695, A293505.

Programs

  • Mathematica
    z = 120; r = 1/2; f[n_] := Fibonacci[n];
Table[Floor[r*f[n]], {n, 0, z}];   (* A004695 *)
Table[Ceiling[r*f[n]], {n, 0, z}]; (* A173173 *)
Table[Round[r*f[n]], {n, 0, z}];   (* A293505 *)

Formula

G.f.: -((x^3 (-1 - x + x^2))/((-1 + x) (1 + x) (1 - x + x^2) (-1 + x + x^2) (1 + x + x^2))).
a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-7) - a(n-8) for n >= 9.
a(n) = floor(1/2 + Fibonacci(n)/2).
a(n) = A004695(n) if (fractional part of Fibonacci(n)/2) < 1/2, otherwise a(n) = A293419(n).
Showing 1-3 of 3 results.

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

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