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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A296691, A296692, A296712.

Sequence in context: A231664 A087916 A359263 * A282585 A280210 A023982

Adjacent sequences: A296690 A296691 A296692 * A296694 A296695 A296696

Keyword

nonn,base

Author

Clark Kimberling, Dec 19 2017

Status

approved