A296752 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144

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 A296751-A296753 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-13 digits of 914 are 5,5,4; here #(rises) = 0 and #(falls) = 1, so 914 is in the sequence.

Mathematica

z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)

Crossrefs

Cf. A296750, A296751, A296712.

Sequence in context: A226051 A238338 A040156 * A297279 A095781 A037974

Adjacent sequences: A296749 A296750 A296751 * A296753 A296754 A296755

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved