A296753 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 211, 224, 225, 238, 239, 240, 252, 253, 254, 255, 266, 267, 268, 269, 270, 280, 281, 282

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 A296753-A296755 partition the natural numbers. See the guide at A296712.

Links

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

Example

The base-14 digits of 1000000 are 2,8,6,2,12; here #(rises) = 2 and #(falls) = 2, so 1000000 is in the sequence.

Mathematica

z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296754 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296755 *)
Select[Range[300], Total[Sign[Differences[IntegerDigits[#, 14]]]]==0&] (* Harvey P. Dale, Sep 20 2022 *)

Crossrefs

Cf. A296754, A296755, A296712.

Sequence in context: A044825 A048311 A043717 * A029959 A297283 A048325

Adjacent sequences: A296750 A296751 A296752 * A296754 A296755 A296756

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved