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%I #9 Jan 27 2023 19:24:23
%S 12,13,14,15,16,17,18,19,23,24,25,26,27,28,29,34,35,36,37,38,39,45,46,
%T 47,48,49,56,57,58,59,67,68,69,78,79,89,112,113,114,115,116,117,118,
%U 119,122,123,124,125,126,127,128,129,133,134,135,136,137,138,139
%N Numbers whose base-10 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 A296712-A296714 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296713/b296713.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-10 digits of 139 are 1,3,9; here #(rises) = 2 and #(falls) = 0, so 139 is in the sequence.
%t z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296713 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296714 *)
%t Select[Range[150],Total[Sign[Differences[IntegerDigits[#]]]]>0&] (* _Harvey P. Dale_, May 21 2021 *)
%Y Cf. A296712, A296714, A296712.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 08 2018
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