A296693 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

3, 6, 7, 9, 12, 18, 21, 22, 24, 25, 27, 30, 33, 34, 36, 39, 48, 54, 57, 60, 61, 63, 64, 65, 66, 67, 69, 70, 72, 75, 76, 78, 79, 81, 84, 87, 88, 90, 93, 99, 102, 103, 105, 106, 108, 111, 114, 115, 117, 120, 129, 144, 147, 156, 162, 165, 168, 169, 171, 174

Offset: 1

Author

Clark Kimberling, Dec 19 2017

Keywords

• nonn
• base

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 A296691-A296693 partition the natural numbers. See the guide at A296712.

Examples

			The base-3 digits of 174 are 2,0,1,1,0; here #(rises) = 1 and #(falls) = 2, so 174 is in the sequence.
		

Links

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

Crossrefs

Cf. A296691, A296692, A296712.

Programs

Mathematica

z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)
rltfQ[n_]:=Module[{d=Differences[IntegerDigits[n,3]]},Count[d,?(#>0&)]<Count[d,?(#<0&)]]; Select[Range[200],rltfQ] (* Harvey P. Dale, Sep 25 2019 *)