A296706 Numbers whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 65, 66, 67, 68, 69, 70, 71, 73, 80, 81, 88, 89, 90, 96, 97, 98, 99, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140

Offset: 1

Author

Clark Kimberling, Jan 08 2018

Keywords

• nonn
• easy
• base

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 A296706-A296707 partition the natural numbers. See the guide at A296712.

Examples

			The base-8 digits of 140 are 2,1,4; here #(rises) = 1 and #(falls) = 1, so 140 is in the sequence.
		

Links

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

Crossrefs

Cf. A296707, A296708, A296712.

Programs

Mathematica

z = 200; b = 8; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296706 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296707 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296708 *)