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%I #10 Mar 01 2024 06:21:08
%S 1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,
%T 2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,
%U 2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2
%N Number of integers m such that 5^n < 3^m < 5^(n+1).
%H Amiram Eldar, <a href="/A022927/b022927.txt">Table of n, a(n) for n = 0..10000</a>
%F Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_3(5) (A113209). - _Amiram Eldar_, Mar 01 2024
%e From _Amiram Eldar_, Mar 01 2024: (Start)
%e a(0) = 1 because 5^0 = 1 < 3^1 = 3 < 5^1 = 5.
%e a(1) = 1 because 5^1 = 5 < 3^2 = 9 < 5^2 = 25.
%e a(2) = 2 because 5^2 = 25 < 3^3 = 27 < 3^4 = 81 < 5^3 = 125. (End)
%t Join[{1}, Differences@ Table[Floor[n * Log[3, 5]], {n, 1, 100}]] (* _Amiram Eldar_, Mar 01 2024 *)
%Y Cf. A022922, A113209.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_
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