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A252229 The number of numbers j*r^k in the interval [n,n+1), where r = (1 + sqrt(5))/2, the golden ratio, and j >=0, k >= 0. 2
1, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 3, 2, 3, 2, 4, 2, 2, 2, 4, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 4, 3, 2, 2, 3, 2, 2, 3, 3, 4, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 2, 2, 3, 2, 3, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The least n for which a(n) = 4 is 29; the least n for which a(n) = 5 is 199.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1 + sum{s(n+1,j) - s(n,j), j=1..floor[(n+1)/r]}, where s(n,j) = floor[log(n/j)/log(r)], for n >= 1.

EXAMPLE

in [0,1):  0

in [1,2):  1, 1 + r

in [2,3):  2, 2 + r

in [3,4):  3, 1+2*r

in [4,5):  4, 1+3*r, 2 + r

MATHEMATICA

z = 100; r = (1 + Sqrt[5])/2;

s[n_, j_] := s[n, j] = Floor[Log[n/j]/Log[r]];

a[n_] := a[n] = Sum[s[n + 1, j] - s[n, j], {j, 1, Floor[(n + 1)/r]}];

t = Join[{1}, Table[1 + a[n], {n, 1, z}]] (* A252229 *)

CROSSREFS

Cf. A182801, A020959.

Sequence in context: A089842 A258569 A091322 * A071215 A164024 A145193

Adjacent sequences:  A252226 A252227 A252228 * A252230 A252231 A252232

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 16 2014

STATUS

approved

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Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.