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A214999 Power floor sequence of sqrt(5). 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 (list; graph; refs; listen; history; text; internal format)
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 * A084635 A294529 A154222

Adjacent sequences:  A214996 A214997 A214998 * A215000 A215001 A215002

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 10 2012

STATUS

approved

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Last modified February 19 06:46 EST 2018. Contains 299330 sequences. (Running on oeis4.)