A372780 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).

1, 3, 5, 8, 10, 13, 15, 17, 20, 22, 25, 27, 29, 32, 34, 37, 39, 41, 44, 46, 49, 51, 54, 56, 58, 61, 63, 66, 68, 70, 73, 75, 78, 80, 82, 85, 87, 90, 92, 94, 97, 99, 102, 104, 107, 109, 111, 114, 116, 119, 121, 123, 126, 128, 131, 133, 135, 138, 140, 143, 145

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

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 this sequence. For n = 2, we have m = 3 and 9 - 8 < 16 - 9, so 2 is in A372779.

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^# &]  (* A372779 *)
Complement[Range[Max[s]], s]   (* this sequence *)

Crossrefs

Cf. A000079, A000244, A056576, A372779 (complement).

Sequence in context: A275813 A356037 A353070 * A080754 A198083 A195168

Adjacent sequences: A372777 A372778 A372779 * A372781 A372782 A372783

Keyword

nonn

Author

Clark Kimberling, May 18 2024

Status

approved