A296713 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 133, 134, 135, 136, 137, 138, 139

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 A296712-A296714 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-10 digits of 139 are 1,3,9; here #(rises) = 2 and #(falls) = 0, so 139 is in the sequence.

Mathematica

z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296713 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296714 *)
Select[Range[150], Total[Sign[Differences[IntegerDigits[#]]]]>0&] (* Harvey P. Dale, May 21 2021 *)

Crossrefs

Cf. A296712, A296714, A296712.

Sequence in context: A162792 A297272 A071589 * A297146 A267761 A324322

Adjacent sequences: A296710 A296711 A296712 * A296714 A296715 A296716

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved