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A372779 Numbers m such that v^n - u^m < u^(m+1) - v^n, where u=2, v=3, and u^m < v^n < u^(m+1).

%I A372779 #8 May 31 2024 14:32:43
%S A372779 2,4,6,7,9,11,12,14,16,18,19,21,23,24,26,28,30,31,33,35,36,38,40,42,
%T A372779 43,45,47,48,50,52,53,55,57,59,60,62,64,65,67,69,71,72,74,76,77,79,81,
%U A372779 83,84,86,88,89,91,93,95,96,98,100,101,103,105,106,108,110
%N A372779 Numbers m such that v^n - u^m < u^(m+1) - v^n, where u=2, v=3, and u^m < v^n < u^(m+1).
%e A372779 The condition u^m < v^n < u^(m + 1) implies m = floor (n*log(v)/log(u)). With u=2 and v=3, for n = 1, we have m = 1 and 3 - 2 >= 4 - 3, so 1 is in A372780. For n = 2, we have m = 3 and 9 - 8 < 16 - 9, so 2 is in this sequence.
%t A372779 z = 200; {u, v} = {2, 3};
%t A372779 m[n_] := Floor[n*Log[v]/Log[u]];
%t A372779 Table[m[n], {n, 0, z}];
%t A372779 s = Select[Range[z], v^# - u^m[#] < u^(m[#] + 1) - v^# &]  (* this sequence *)
%t A372779 Complement[Range[Max[s]], s]   (* A372780 *)
%Y A372779 Cf. A000079, A000244, A056576, A372780 (complement).
%K A372779 nonn
%O A372779 1,1
%A A372779 _Clark Kimberling_, May 18 2024