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.

A293313 Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

1, 3, 6, 12, 25, 51, 103, 207, 414, 828, 1656, 3313, 6627, 13254, 26509, 53019, 106039, 212078, 424157, 848315, 1696631, 3393263, 6786526, 13573052, 27146105, 54292211, 108584422, 217168845, 434337691, 868675383, 1737350766, 3474701532, 6949403065
Offset: 0

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Author

Clark Kimberling, Oct 06 2017

Keywords

Crossrefs

Programs

  • Maple
    A293313:=n->floor(2^n*(1+sqrt(5))/2): seq(A293313(n), n=0..40); # Wesley Ivan Hurt, Oct 06 2017
  • Mathematica
    z = 120; r = GoldenRatio;
    Table[Floor[r*2^n], {n, 0, z}];   (* A293313 *)
    Table[Ceiling[r*2^n], {n, 0, z}]; (* A293314 *)
    Table[Round[r*2^n], {n, 0, z}];   (* A293315 *)
  • PARI
    a(n) = (2^n*(1+sqrt(5)))\2; \\ Altug Alkan, Oct 06 2017

Formula

a(n) = floor(r*2^n), where r = (1+sqrt(5))/2.
a(n) = A293314(n) - 1.