A325913 - OEIS

%I #45 Dec 22 2021 10:18:00

%S 1,3,5,6,8,10,11,13,15,17,18,20,22,23,25,27,29,30,32,34,35,37,39,41,

%T 42,44,46,47,49,51,52,54,56,58,59,61,63,64,66,68,70,71,73,75,76,78,80,

%U 82,83,85,87,88,90,92,94,95,97,99,100

%N Integers m such that there are exactly two powers of 2 between 3^m and 3^(m+1).

%C Or m such that A022921(m) = 2.

%C Also largest m such that 2^(m+n) > 3^m. - _Bob Selcoe_, Dec 19 2021

%H Benjamin Lombardo, <a href="/A325913/b325913.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(n/(log_2(3)-1)).

%F a(n) = A054414(n) - n - 1.

%e For m=3, there are exactly two powers of 2 between 3^3 = 27 and 3^(3+1) = 81: 32 and 64, since 27 < 32 < 64 < 81. Therefore, m=3 is an element of the sequence (at n=2).

%o (Python)

%o import math

%o def a(n):

%o     return math.floor(n/(math.log2(3)-1))

%o for n in range(1, 101):

%o     print("a(" + str(n) + ") = " + str(a(n)))

%Y Cf. A022921, A054414.

%K nonn

%O 1,2

%A _Benjamin Lombardo_, Sep 08 2019