A296751 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 49, 50, 51, 57, 58, 59, 60, 61, 62, 63, 64, 71, 72, 73, 74, 75, 76, 77, 85, 86, 87, 88, 89, 90, 99, 100, 101, 102, 103, 113, 114, 115, 116, 127, 128

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 1000 are 5,11,12; here #(rises) = 2 and #(falls) = 0, so 1000 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, A296752, A296712.

Sequence in context: A291575 A004504 A363784 * A297281 A176294 A214424

Adjacent sequences: A296748 A296749 A296750 * A296752 A296753 A296754

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved