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A296750 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

%I A296750 #7 Jan 27 2023 19:25:41
%S A296750 1,2,3,4,5,6,7,8,9,10,11,12,14,28,42,56,70,84,98,112,126,140,154,168,
%T A296750 170,171,172,173,174,175,176,177,178,179,180,181,183,195,196,208,209,
%U A296750 210,221,222,223,224,234,235,236,237,238,247,248,249,250,251,252
%N A296750 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
%C A296750 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 A296750-A296751 partition the natural numbers. See the guide at A296712.
%H A296750 Clark Kimberling, <a href="/A296750/b296750.txt">Table of n, a(n) for n = 1..10000</a>
%e A296750 The base-13 digits of 998 are 5,11,10; here #(rises) = 1 and #(falls) = 1, so 998 is in the sequence.
%t A296750 z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t A296750 Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
%t A296750 Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)
%t A296750 Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)
%Y A296750 Cf. A296751, A296752, A296712.
%K A296750 nonn,base,easy
%O A296750 1,2
%A A296750 _Clark Kimberling_, Jan 08 2018