A214999 Power floor sequence of sqrt(5).

2, 4, 8, 17, 38, 84, 187, 418, 934, 2088, 4668, 10437, 23337, 52183, 116684, 260913, 583419, 1304564, 2917093, 6522818, 14585464, 32614088, 72927317, 163070438, 364636584, 815352188, 1823182917, 4076760937, 9115914583

Offset

0,1

Comments

See A214992 for a discussion of power floor sequence and the power floor function, p1(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = sqrt(5), and the limit p1(r) = 1.4935514451954997630823098687087959696356...

Links

Clark Kimberling, Table of n, a(n) for n = 0..250

Formula

a(n) = [x*a(n-1)], where x=sqrt(5), a(0) = [x].

Example

a(0) = [r] = 2, where r = sqrt(5); a(1) = [2*r] = 4; a(2) = [4*r] = 8.

Mathematica

x = Sqrt[5]; z = 30; (* z = # terms in sequences *)
f[x_] := Floor[x]; c[x_] := Ceiling[x];
p1[0] = f[x]; p2[0] = f[x]; p3[0] = c[x]; p4[0] = c[x];
p1[n_] := f[x*p1[n - 1]]
p2[n_] := If[Mod[n, 2] == 1, c[x*p2[n - 1]], f[x*p2[n - 1]]]
p3[n_] := If[Mod[n, 2] == 1, f[x*p3[n - 1]], c[x*p3[n - 1]]]
p4[n_] := c[x*p4[n - 1]]
Table[p1[n], {n, 0, z}]  (* A214999 *)
Table[p2[n], {n, 0, z}]  (* A215091 *)
Table[p3[n], {n, 0, z}]  (* A218982 *)
Table[p4[n], {n, 0, z}]  (* A218983 *)

Crossrefs

Cf. A214992, A215091, A218982, A218983.

Sequence in context: A087803 A212658 A036374 * A348756 A348755 A084635

Adjacent sequences: A214996 A214997 A214998 * A215000 A215001 A215002

Keyword

nonn,easy

Author

Clark Kimberling, Nov 10 2012

Status

approved