A022927 Number of integers m such that 5^n < 3^m < 5^(n+1).

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, 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, 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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Examples

			From _Amiram Eldar_, Mar 01 2024: (Start)
a(0) = 1 because 5^0 = 1 < 3^1 = 3 < 5^1 = 5.
a(1) = 1 because 5^1 = 5 < 3^2 = 9 < 5^2 = 25.
a(2) = 2 because 5^2 = 25 < 3^3 = 27 < 3^4 = 81 < 5^3 = 125. (End)
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A022922, A113209.

Programs

Mathematica

Join[{1}, Differences@ Table[Floor[n * Log[3, 5]], {n, 1, 100}]] (* Amiram Eldar, Mar 01 2024 *)

Formula

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_3(5) (A113209). - Amiram Eldar, Mar 01 2024