A296753 Numbers whose base-14 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, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 211, 224, 225, 238, 239, 240, 252, 253, 254, 255, 266, 267, 268, 269, 270, 280, 281, 282

Offset: 1

Author

Clark Kimberling, Jan 08 2018

Keywords

• nonn
• base
• easy

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 A296753-A296755 partition the natural numbers. See the guide at A296712.

Examples

			The base-14 digits of 1000000 are 2,8,6,2,12; here #(rises) = 2 and #(falls) = 2, so 1000000 is in the sequence.
		

Links

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

Crossrefs

Cf. A296754, A296755, A296712.

Programs

Mathematica

z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296754 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296755 *)
Select[Range[300],Total[Sign[Differences[IntegerDigits[#,14]]]]==0&] (* Harvey P. Dale, Sep 20 2022 *)