A296699 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 25, 30, 50, 55, 56, 60, 61, 75, 80, 81, 85, 86, 87, 90, 91, 92, 100, 105, 106, 110, 111, 112, 115, 116, 117, 118, 120, 121, 122, 123, 125, 130, 135, 136, 140, 141, 142, 145, 146, 147, 148, 150, 155, 180, 205, 210, 211

Offset: 1

Author

Clark Kimberling, Dec 21 2017

Keywords

• nonn
• 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 A296697-A296699 partition the natural numbers. See the guide at A296712.

Examples

			The base-5 digits of 211 are 1,3,2,1; here #(rises) = 1 and #(falls) = 2, so 211 is in the sequence.
		

Links

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

Crossrefs

Cf. A296697, A296698, A296712.

Programs

Mathematica

z = 200; b = 5; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296697 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296698 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296699 *)