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).

2, 4, 6, 7, 9, 11, 12, 14, 16, 18, 19, 21, 23, 24, 26, 28, 30, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 89, 91, 93, 95, 96, 98, 100, 101, 103, 105, 106, 108, 110

Offset: 1

Author

Clark Kimberling, May 18 2024

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000079, A000244, A056576, A372780 (complement).

Programs

Mathematica

z = 200; {u, v} = {2, 3};
m[n_] := Floor[n*Log[v]/Log[u]];
Table[m[n], {n, 0, z}];
s = Select[Range[z], v^# - u^m[#] < u^(m[#] + 1) - v^# &]  (* this sequence *)
Complement[Range[Max[s]], s]   (* A372780 *)