A022923 Number of integers m such that 7^n < 2^m < 7^(n+1).

2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Examples

			From _Amiram Eldar_, Mar 01 2024: (Start)
a(0) = 2 because 7^0 = 1 < 2^1 = 2 < 2^2 = 4 < 7^1 = 7.
a(1) = 3 because 7^1 = 7 < 2^3 = 8 < 2^4 = 16 < 2^3 = 32 < 7^2 = 49.
a(2) = 3 because 7^2 = 49 < 2^6 = 64 < 2^7 = 128 < 2^8 = 256 < 7^3 = 343. (End)
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A020860, A022921, A022922.

Programs

Mathematica

Differences[Floor[Log2[7^Range[0,100]]]] (* Harvey P. Dale, Jun 23 2019 *)

Formula

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_2(7) (A020860). - Amiram Eldar, Mar 01 2024