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A296712 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

%I A296712 #7 Jan 27 2023 19:24:14
%S A296712 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,102,103,104,105,106,
%T A296712 107,108,109,111,120,121,130,131,132,140,141,142,143,150,151,152,153,
%U A296712 154,160,161,162,163,164,165,170,171,172,173,174,175,176,180,181
%N A296712 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
%C A296712 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.
%C A296712 ****
%C A296712 Guide to related sequences:
%C A296712 Base   #(rises) = #(falls)   #(rises) > #(falls)   #(rises) < #(falls)
%C A296712 2            A005408             (none)                A005843
%C A296712 3            A296691             A296692               A296693
%C A296712 4            A296694             A296695               A296696
%C A296712 5            A296697             A296698               A296699
%C A296712 6            A296700             A296701               A296702
%C A296712 7            A296703             A296704               A296705
%C A296712 8            A296706             A296707               A296708
%C A296712 9            A296709             A296710               A296711
%C A296712 10           A296712             A296713               A296714
%C A296712 11           A296744             A296745               A296746
%C A296712 12           A296747             A296748               A296749
%C A296712 13           A296750             A296751               A296752
%C A296712 14           A296753             A296754               A296755
%C A296712 15           A296756             A296757               A296758
%C A296712 16           A296759             A296760               A296761
%C A296712 20           A296762             A296763               A296764
%C A296712 60           A296765             A296766               A296767
%H A296712 Clark Kimberling, <a href="/A296712/b296712.txt">Table of n, a(n) for n = 1..10000</a>
%e A296712 The base-10 digits of 181 are 1,8,1; here #(rises) = 1 and #(falls) = 1, so 181 is in the sequence.
%t A296712 z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t A296712 Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
%t A296712 Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296713 *)
%t A296712 Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296714 *)
%Y A296712 Cf. A296713, A296714, A296712.
%K A296712 nonn,base,easy
%O A296712 1,2
%A A296712 _Clark Kimberling_, Jan 08 2018