%I #7 Jan 27 2023 19:26:43
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,32,48,64,80,96,112,128,144,160,
%T 176,192,208,224,226,227,228,229,230,231,232,233,234,235,236,237,238,
%U 239,241,255,256,270,271,272,285,286,287,288,300,301,302,303,304
%N Numbers whose base15 digits d(m), d(m1), ..., 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 A296756A296758 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296756/b296756.txt">Table of n, a(n) for n = 1..10000</a>
%e The base15 digits of 2^20 are 1, 5, 10, 10, 5, 1; here #(rises) = 2 and #(falls) = 2, so 2^20 is in the sequence.
%t z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], 1] == Count[d[#], 1] &] (* A296756 *)
%t Select[Range [z], Count[d[#], 1] < Count[d[#], 1] &] (* A296757 *)
%t Select[Range [z], Count[d[#], 1] > Count[d[#], 1] &] (* A296758 *)
%Y Cf. A296757, A296758, A296712.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 08 2018
