A296710 Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 111, 112, 113, 114, 115, 116, 121, 122, 123, 124, 125, 131, 132, 133, 134, 141, 142

Offset

1,1

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 142 are 1,6,7; here #(rises) = 2 and #(falls) = 0, so 142 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. A296709, A296711, A296712.

Sequence in context: A110403 A119247 A297269 * A297143 A138595 A192271

Adjacent sequences: A296707 A296708 A296709 * A296711 A296712 A296713

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved