A296756 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 255, 256, 270, 271, 272, 285, 286, 287, 288, 300, 301, 302, 303, 304

Offset

1,2

Comments

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296756-A296758 partition the natural numbers. See the guide at A296712.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

The base-15 digits of 2^20 are 1, 5, 10, 10, 5, 1; here #(rises) = 2 and #(falls) = 2, so 2^20 is in the sequence.

Mathematica

z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296757 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296758 *)

Crossrefs

Cf. A296757, A296758, A296712.

Sequence in context: A044826 A048312 A043718 * A029960 A297286 A048326

Adjacent sequences: A296753 A296754 A296755 * A296757 A296758 A296759

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved