%I #5 Dec 18 2014 23:09:22
%S 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,
%T 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,
%U 3,2,2,3,3,2,2,3,4,3,2,2,3,2,3,2,3,2
%N 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.
%C The least n for which a(n) = 4 is 29; the least n for which a(n) = 5 is 199.
%H Clark Kimberling, <a href="/A252229/b252229.txt">Table of n, a(n) for n = 0..1000</a>
%F 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.
%e in [0,1): 0
%e in [1,2): 1, 1 + r
%e in [2,3): 2, 2 + r
%e in [3,4): 3, 1+2*r
%e in [4,5): 4, 1+3*r, 2 + r
%t z = 100; r = (1 + Sqrt[5])/2;
%t s[n_, j_] := s[n, j] = Floor[Log[n/j]/Log[r]];
%t a[n_] := a[n] = Sum[s[n + 1, j] - s[n, j], {j, 1, Floor[(n + 1)/r]}];
%t t = Join[{1}, Table[1 + a[n], {n, 1, z}]] (* A252229 *)
%Y Cf. A182801, A020959.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Dec 16 2014