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%I #9 Jan 28 2023 19:37:40
%S 4,8,9,12,13,14,16,20,32,36,37,40,41,48,52,53,56,57,58,60,61,62,64,68,
%T 72,73,76,77,78,80,84,100,116,120,121,128,132,136,137,140,141,142,144,
%U 145,146,147,148,149,152,153,156,157,158,160,164,165,168,169
%N Numbers whose base-4 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 A296694-A296696 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296696/b296696.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-4 digits of 196 are 3,0,1,0; here #(rises) = 1 and #(falls) = 2, so 196 is in the sequence.
%t z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296695 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296696 *)
%Y Cf. A296694, A296695, A296712.
%K nonn,base
%O 1,1
%A _Clark Kimberling_, Dec 21 2017
%E Example corrected by _Harvey P. Dale_, Sep 04 2018
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