A296697 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 6, 12, 18, 24, 26, 27, 28, 29, 31, 35, 36, 40, 41, 42, 45, 46, 47, 48, 51, 52, 53, 54, 57, 58, 59, 62, 65, 66, 67, 70, 71, 72, 73, 76, 77, 78, 79, 82, 83, 84, 88, 89, 93, 95, 96, 97, 98, 101, 102, 103, 104, 107, 108, 109, 113, 114, 119, 124, 126

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 126 are 1,0,0,1; here #(rises) = 1 and #(falls) = 1, so 126 is in the sequence.
		

Links

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

Crossrefs

Cf. A296698, A296699, 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 *)
Select[Range[130],Total[Sign[Differences[IntegerDigits[#,5]]]]==0&] (* Harvey P. Dale, Jul 30 2019 *)