A296693 - OEIS

%I #12 Jan 28 2023 19:35:28

%S 3,6,7,9,12,18,21,22,24,25,27,30,33,34,36,39,48,54,57,60,61,63,64,65,

%T 66,67,69,70,72,75,76,78,79,81,84,87,88,90,93,99,102,103,105,106,108,

%U 111,114,115,117,120,129,144,147,156,162,165,168,169,171,174

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

%C 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.

%H Clark Kimberling, <a href="/A296693/b296693.txt">Table of n, a(n) for n = 1..10000</a>

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

%t z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)

%t rltfQ[n_]:=Module[{d=Differences[IntegerDigits[n,3]]},Count[d,_?(#>0&)]<Count[d,_?(#<0&)]]; Select[Range[200],rltfQ] (* _Harvey P. Dale_, Sep 25 2019 *)

%Y Cf. A296691, A296692, A296712.

%K nonn,base

%O 1,1

%A _Clark Kimberling_, Dec 19 2017