A296709 Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 82, 83, 84, 85, 86, 87, 88, 89, 91, 99, 100, 108, 109, 110, 117, 118, 119, 120, 126, 127, 128, 129, 130, 135, 136, 137, 138, 139, 140, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 158

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 A296709-A296711 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-9 digits of 158 are 1,8,5; here #(rises) = 1 and #(falls) = 1, so 158 is in the sequence.

Mathematica

z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296709 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296710 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296711 *)

Crossrefs

Cf. A296710, A296711, A296712.

Sequence in context: A044820 A048306 A043712 * A029955 A297268 A048320

Adjacent sequences: A296706 A296707 A296708 * A296710 A296711 A296712

Keyword

nonn,easy,base

Author

Clark Kimberling, Jan 08 2018

Status

approved