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%I #7 Jan 27 2023 19:23:47
%S 11,12,13,14,15,16,17,21,22,23,24,25,26,31,32,33,34,35,41,42,43,44,51,
%T 52,53,61,62,71,92,93,94,95,96,97,98,101,102,103,104,105,106,107,111,
%U 112,113,114,115,116,121,122,123,124,125,131,132,133,134,141,142
%N Numbers whose base-9 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 A296709-A296711 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296710/b296710.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-9 digits of 142 are 1,6,7; here #(rises) = 2 and #(falls) = 0, so 142 is in the sequence.
%t z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296709 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296710 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296711 *)
%Y Cf. A296709, A296711, A296712.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 08 2018
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