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%I #7 Jan 27 2023 19:08:52
%S 1,2,3,4,5,6,8,16,24,32,40,48,50,51,52,53,54,55,57,63,64,70,71,72,77,
%T 78,79,80,84,85,86,87,88,91,92,93,94,95,96,99,100,101,102,103,104,107,
%U 108,109,110,111,114,119,120,121,126,127,128,129,133,134,135
%N Numbers whose base-7 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 A296703-A296705 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296703/b296703.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-7 digits of 135 are 2,5,2; here #(rises) = 1 and #(falls) = 1, so 135 is in the sequence.
%t z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296704 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296705 *)
%Y Cf. A296704, A296705, A296712.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Jan 07 2018
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