A022923 - OEIS

%I #11 Mar 01 2024 06:24:12

%S 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,

%T 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,

%U 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

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

%H Harvey P. Dale, <a href="/A022923/b022923.txt">Table of n, a(n) for n = 0..1000</a>

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

%e From _Amiram Eldar_, Mar 01 2024: (Start)

%e a(0) = 2 because 7^0 = 1 < 2^1 = 2 < 2^2 = 4 < 7^1 = 7.

%e a(1) = 3 because 7^1 = 7 < 2^3 = 8 < 2^4 = 16 < 2^3 = 32 < 7^2 = 49.

%e a(2) = 3 because 7^2 = 49 < 2^6 = 64 < 2^7 = 128 < 2^8 = 256 < 7^3 = 343. (End)

%t Differences[Floor[Log2[7^Range[0,100]]]] (* _Harvey P. Dale_, Jun 23 2019 *)

%Y Cf. A020860, A022921, A022922.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_