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

%I A296693 #12 Jan 28 2023 19:35:28
%S A296693 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 A296693 66,67,69,70,72,75,76,78,79,81,84,87,88,90,93,99,102,103,105,106,108,
%U A296693 111,114,115,117,120,129,144,147,156,162,165,168,169,171,174
%N A296693 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.
%C A296693 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 A296693 Clark Kimberling, <a href="/A296693/b296693.txt">Table of n, a(n) for n = 1..10000</a>
%e A296693 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 A296693 z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t A296693 Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
%t A296693 Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
%t A296693 Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)
%t 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 *)
%Y A296693 Cf. A296691, A296692, A296712.
%K A296693 nonn,base
%O A296693 1,1
%A A296693 _Clark Kimberling_, Dec 19 2017